# TrueScalers — full tool reference > Free browser-based calculators and converters. Every calculation runs locally in your browser — no data is uploaded, stored, or sent to a server. Published by TrueScalers (syedaqeel185@gmail.com). 40 tools. Each entry below gives the definitive answer, the formula, a worked example, and the sources the method is drawn from. --- ## Calculators TrueScalers publishes 16 free calculators covering mortgages, loans, compound interest, percentages, sales tax, BMI, daily calories, body fat, age and grades. Every calculator shows the formula it applies, defines each variable, and computes entirely inside the browser, so no financial or health figure is ever transmitted. ### Percentage calculator URL: https://truescalers.com/calculators/percentage-calculator Last reviewed: 2026-08-09 A percentage calculator finds what one number is as a proportion of another, scaled to 100. The percentage of a value is calculated as (X ÷ 100) × Y, so 15% of 200 equals 30. Percentage change from an old value to a new value is ((new − old) ÷ |old|) × 100, so 80 rising to 100 is a 25% increase. Formula: result = (X ÷ 100) × Y change = ((Y − X) ÷ |X|) × 100 X = The percentage, or the starting value when calculating change. Y = The base value the percentage is taken of, or the ending value when calculating change. result = The portion of Y represented by X percent. change = The percentage difference between the starting and ending values, signed. Worked example — Calculation: What is 15% of 200?, X: 15, Y: 200 → 30 Convert the percentage to a decimal multiplier by dividing by 100: 15 ÷ 100 = 0.15. Multiply that multiplier by the base value: 0.15 × 200 = 30. So 15% of 200 is 30, and the remaining 85% is 170. Reversing the calculation confirms the result: 30 ÷ 200 = 0.15, which is 15%. Questions answered on this page: Q: How do you calculate a percentage of a number? A: Divide the percentage by 100 to get a decimal multiplier, then multiply that multiplier by the number. For 15% of 200, divide 15 by 100 to get 0.15, then multiply 0.15 by 200 to get 30. The same method works for percentages above 100: 250% of 40 is 2.5 × 40, which equals 100. Q: What is the difference between percentage change and percentage difference? A: Percentage change has a designated starting value and is calculated as ((new − old) ÷ |old|) × 100, so it is directional and signed. Percentage difference is symmetric and compares two values against their mean, calculated as (|a − b| ÷ ((a + b) ÷ 2)) × 100. Change answers "how much did it move"; difference answers "how far apart are they". Q: Why is a 50% decrease not reversed by a 50% increase? A: Percentages apply to whatever value is current, not to the original. A 50% decrease takes 100 down to 50. A 50% increase then applies to 50, not to 100, and adds only 25, giving 75. Reversing a 50% decrease requires a 100% increase. This asymmetry is why stacked discounts multiply rather than add. Q: How do you work out the original price before a discount? A: Divide the discounted price by one minus the discount as a decimal. An item selling for $80 after a 20% discount had an original price of 80 ÷ (1 − 0.20), which is 80 ÷ 0.8, or $100. For a price after an increase, divide by one plus the rate instead: $120 after a 20% markup was originally 120 ÷ 1.2, or $100. Q: What is a percentage point and how does it differ from a percent? A: A percentage point is the arithmetic difference between two percentages. An interest rate moving from 4% to 6% has risen by 2 percentage points, but by 50 percent. Financial and statistical reporting uses percentage points precisely to avoid this ambiguity. Confusing the two overstates or understates change by a large margin whenever the base rate is small. Q: Can a percentage be greater than 100 or negative? A: Yes to both. A percentage above 100 simply means the part exceeds the whole, which is normal for growth figures: revenue tripling is a 200% increase. A negative percentage indicates a decrease. Only proportions of a fixed total — such as a share of votes cast — are structurally capped at 100%. Q: How do you convert a percentage to a fraction or a decimal? A: To convert to a decimal, divide by 100: 37.5% becomes 0.375. To convert to a fraction, write the percentage over 100 and reduce: 37.5% becomes 37.5/100, which reduces to 3/8. To go the other way, multiply a decimal by 100 and add a percent sign: 0.045 becomes 4.5%. Sources: - Percentage — definition and worked methods — Encyclopædia Britannica — https://www.britannica.com/science/percentage - Percentage change and percentage point guidance — UK Office for National Statistics — https://www.ons.gov.uk/methodology/methodologytopicsandstatisticalconcepts - Ratios, rates and percentages — mathematical standards — Common Core State Standards Initiative — https://www.thecorestandards.org/Math/Content/RP/ --- ### Mortgage calculator URL: https://truescalers.com/calculators/mortgage-calculator Last reviewed: 2026-08-09 A mortgage calculator estimates a monthly payment from the loan principal, annual interest rate, and term using the amortization formula M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1], where r is the monthly rate and n is the total number of payments. A $320,000 loan at 6.5% over 30 years gives a principal-and-interest payment of $2,022.62 per month. Formula: M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1] M = The level monthly payment covering principal and interest. P = The loan principal — the home price minus the down payment. r = The periodic interest rate: the annual nominal rate divided by 100, then divided by 12. n = The total number of monthly payments, equal to the term in years multiplied by 12. Worked example — Home price: $400,000, Down payment: $80,000 (20%), Interest rate: 6.5%, Term: 30 years, Property tax: $4,800 per year, Home insurance: $1,800 per year → $2,022.62 principal and interest, $2,572.62 total monthly The loan principal is $400,000 − $80,000 = $320,000. The monthly rate r is 6.5 ÷ 100 ÷ 12 = 0.00541667, and n is 30 × 12 = 360 payments. Substituting: (1 + r)ⁿ = 6.99179, so M = 320,000 × (0.00541667 × 6.99179) ÷ (6.99179 − 1) = $2,022.62. Escrow adds $4,800 ÷ 12 = $400 of tax and $1,800 ÷ 12 = $150 of insurance, giving $2,572.62 per month. Over the full term, total interest reaches $408,142. Questions answered on this page: Q: What is the formula for a monthly mortgage payment? A: The standard amortization formula is M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. P is the loan principal, r is the monthly interest rate found by dividing the annual rate by 12, and n is the total number of monthly payments. The formula produces a level payment in which the interest share falls and the principal share rises over the life of the loan. Q: What does PITI mean in a mortgage payment? A: PITI stands for principal, interest, taxes and insurance — the four components of a fully escrowed monthly housing payment. Principal and interest repay the loan itself. Taxes and insurance are collected by the servicer and paid on the borrower's behalf. Lenders assess affordability against PITI, not against principal and interest alone. Q: How much does a 1% higher interest rate cost on a mortgage? A: On a $320,000 loan over 30 years, moving from 6.5% to 7.5% raises the monthly payment from $2,022.62 to $2,237.49, an increase of $214.87 per month. Across the full 360 payments that difference totals $77,353 in additional interest. Rate sensitivity rises with both the principal and the term. Q: Does making one extra mortgage payment a year make a difference? A: Substantially. On a $320,000 loan at 6.5% over 30 years, adding $170 a month — roughly one extra payment a year — clears the loan in 290 months instead of 360. That is five years and ten months early, and it saves $93,667 in interest. Extra payments apply entirely to principal, which reduces every interest charge that follows. Q: What is private mortgage insurance and when does it apply? A: Private mortgage insurance protects the lender when the down payment is below 20% of the home value. It typically costs between 0.3% and 1.5% of the original loan amount each year. Under the US Homeowners Protection Act, a borrower may request cancellation at 80% loan-to-value, and the servicer must terminate it automatically at 78%. Q: Is a 15-year or a 30-year mortgage cheaper? A: A 15-year mortgage costs far less in total interest but requires a much higher monthly payment. A $320,000 loan at 6.5% costs $2,022.62 a month over 30 years and $2,787.54 a month over 15 years, but total interest falls from $408,142 to $181,758. Fifteen-year loans also usually carry a lower quoted rate. Q: Why does so little of an early mortgage payment reduce the balance? A: Interest is charged on the outstanding balance, which is at its largest at the start. On a $320,000 loan at 6.5%, the first payment of $2,022.62 includes $1,733.33 of interest and only $289.29 of principal. The principal share grows every month, and first exceeds half the payment at month 233 of the 360-payment term. Sources: - Understanding loan estimates and mortgage costs — US Consumer Financial Protection Bureau — https://www.consumerfinance.gov/owning-a-home/loan-estimate/ - Homeowners Protection Act — PMI cancellation rules — US Federal Reserve — https://www.federalreserve.gov/boarddocs/supmanual/cch/pmi.pdf - Primary Mortgage Market Survey — historical rates — Freddie Mac — https://www.freddiemac.com/pmms --- ### Loan calculator URL: https://truescalers.com/calculators/loan-calculator Last reviewed: 2026-08-09 A loan calculator finds the level monthly payment on a fixed-rate loan using M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1], where P is the amount borrowed, r is the annual rate divided by 12, and n is the number of monthly payments. A $20,000 loan at 9.5% over 5 years costs $420.04 per month and $5,202 in total interest. Formula: M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1] M = The level monthly payment. P = The principal — the amount borrowed at the start. r = The monthly interest rate: the annual percentage rate divided by 100, then by 12. n = The total number of monthly payments: the term in years multiplied by 12. Worked example — Loan amount: $20,000, Annual rate: 9.5%, Term: 5 years, Extra monthly payment: $0 → $420.04 per month The monthly rate r is 9.5 ÷ 100 ÷ 12 = 0.00791667, and n is 5 × 12 = 60 payments. Raising (1 + r) to the 60th power gives 1.60586. Substituting into the formula: M = 20,000 × (0.00791667 × 1.60586) ÷ (1.60586 − 1) = 20,000 × 0.01271305 ÷ 0.60586 = $420.04. Across all 60 payments the borrower repays $25,202, of which $5,202 is interest — 26% of the amount borrowed. Questions answered on this page: Q: How is a loan payment calculated? A: A fixed-rate loan payment is calculated with the amortization formula M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. The result is a level payment that fully repays both principal and interest by the final instalment. Early payments are mostly interest because interest accrues on a large outstanding balance; later payments are mostly principal. Q: What is the difference between interest rate and APR? A: The interest rate is the cost of borrowing the principal alone. The annual percentage rate additionally includes lender fees, points and certain closing costs, expressed as a yearly rate. US Regulation Z requires lenders to disclose APR precisely so that offers with different fee structures can be compared on one number. Q: Does paying a loan off early save money? A: Almost always, because interest accrues on the outstanding balance each month. Repaying early reduces the balance sooner and every subsequent interest charge with it. The exception is a loan with a prepayment penalty or one using the Rule of 78s, an interest-front-loading method now restricted for most consumer loans in the United States. Q: What is amortization? A: Amortization is the process of repaying a debt through scheduled level payments that cover both interest and principal. Each payment first covers the interest accrued that period, and the remainder reduces the balance. Because the balance falls, the interest portion shrinks every period and the principal portion grows by the same amount. Q: How much does a longer loan term actually cost? A: A longer term lowers the monthly payment but raises total interest. A $20,000 loan at 9.5% costs $420.04 a month over 5 years with $5,202 of interest, or $632.07 a month over 3 years with $2,754 of interest. The three-year term costs $212 more each month and saves $2,448 overall. Q: What is a simple interest loan? A: A simple interest loan charges interest on the outstanding principal only, never on accumulated interest. Most consumer instalment loans work this way, which is why paying a few days early reduces the interest charged. Compound interest, by contrast, charges interest on previously accrued interest and is the norm for credit-card balances. Sources: - Regulation Z — Truth in Lending disclosures — US Consumer Financial Protection Bureau — https://www.consumerfinance.gov/rules-policy/regulations/1026/ - What is an APR? — US Consumer Financial Protection Bureau — https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/ - Consumer credit statistics — G.19 release — US Federal Reserve — https://www.federalreserve.gov/releases/g19/current/ --- ### Car payment calculator URL: https://truescalers.com/calculators/car-payment-calculator Last reviewed: 2026-08-09 A car payment calculator finds the monthly cost of an auto loan from the amount financed, the annual percentage rate and the term in months, using M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. Financing $28,000 at 7.2% APR over 60 months produces a payment of $557.08 per month and $5,425 in total interest. Formula: P = price + sales tax − down payment − trade-in; M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1] P = The amount financed after the deposit, trade-in credit and sales tax are applied. M = The level monthly car payment. r = The monthly rate: the APR divided by 100, then by 12. n = The term in months. Worked example — Vehicle price: $32,000, Down payment: $4,000, Trade-in value: $0, APR: 7.2%, Term: 60 months, Sales tax: 0% → $557.08 per month The amount financed is $32,000 − $4,000 = $28,000. The monthly rate r is 7.2 ÷ 100 ÷ 12 = 0.006, and n is 60. Raising (1.006) to the 60th power gives 1.43128. Substituting: M = 28,000 × (0.006 × 1.43128) ÷ (1.43128 − 1) = $557.08. Across 60 payments the total repaid is $33,425, so interest costs $5,425 — about 19% of the amount financed. Questions answered on this page: Q: How much should a car down payment be? A: A deposit of 20% on a new car and 10% on a used car is the conventional guideline. A larger deposit reduces the financed balance, lowers total interest, and shortens the period during which the loan exceeds the vehicle value. Because new cars depreciate fastest in the first year, a small deposit frequently produces immediate negative equity. Q: Is a 72-month or 84-month car loan a bad idea? A: Long terms lower the monthly payment but raise total interest and extend the period of negative equity. Financing $28,000 at 7.2% costs $557.08 a month over 60 months with $5,425 of interest, or $477.94 a month over 72 months with $6,612 of interest. The longer term saves $79 a month and costs $1,187 more overall. Q: What credit score is needed for the best auto loan rate? A: Lenders generally reserve their lowest advertised rates for scores of 720 and above, using the FICO Auto Score range of 250 to 900 or the standard 300 to 850 range. Borrowers in the 660 to 719 band typically pay two to four percentage points more, and subprime borrowers below 600 often pay in excess of 15% APR. Q: Should sales tax be rolled into the car loan? A: Rolling sales tax into the loan preserves cash today but adds to the financed balance and therefore accrues interest for the whole term. On a $32,000 car with 7% tax, financing the $2,240 tax bill at 7.2% over 60 months costs an extra $434 in interest compared with paying it at signing. Q: What does negative equity on a car loan mean? A: Negative equity, or being upside-down, means the outstanding loan balance exceeds what the vehicle would sell for. It arises because a new car typically loses 20% of its value in the first year while the loan balance falls more slowly. Gap insurance covers the shortfall if the vehicle is written off during that period. Q: Does dealer financing or a bank loan cost less? A: Neither is systematically cheaper. Manufacturer captive-finance arms sometimes offer subsidised promotional rates well below market, while dealers may also mark up a third-party lender's rate as compensation. Obtaining a pre-approval from a bank or credit union before visiting the dealership establishes a benchmark the dealer must beat. Sources: - Auto loans — shopping and comparison guidance — US Consumer Financial Protection Bureau — https://www.consumerfinance.gov/consumer-tools/auto-loans/ - Understanding vehicle financing — US Federal Trade Commission — https://consumer.ftc.gov/articles/financing-or-leasing-car - Consumer credit — auto loan terms and rates — US Federal Reserve — https://www.federalreserve.gov/releases/g19/current/ --- ### Compound interest calculator URL: https://truescalers.com/calculators/compound-interest-calculator Last reviewed: 2026-08-09 Compound interest pays a return on both the original principal and on all previously accrued interest. The balance after t years is A = P(1 + r/n)^(nt), extended by PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)] when contributions are added each period. $5,000 growing at 7% with $300 added monthly reaches $176,472 after 20 years. Formula: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)] A = The final balance after t years. P = The starting principal. r = The annual rate as a decimal — 7% is entered as 0.07. n = The number of compounding periods per year. t = The number of years the money is invested. PMT = The amount added at the end of each compounding period. Worked example — Starting amount: $5,000, Added each month: $300, Annual return: 7%, Years: 20, Compounding: Monthly → $176,472 The periodic rate r/n is 0.07 ÷ 12 = 0.00583333, and nt is 240 periods. The growth factor (1.00583333)^240 equals 4.03874. The starting $5,000 grows to 5,000 × 4.03874 = $20,194. The contributions form an annuity worth 300 × (4.03874 − 1) ÷ 0.00583333 = $156,278. Adding the two gives $176,472. Total money contributed is $5,000 + $72,000 = $77,000, so $99,472 — 56% of the final balance — is compound interest. Questions answered on this page: Q: What is the compound interest formula? A: The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years. Regular contributions add the annuity term PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]. Q: What is the difference between simple and compound interest? A: Simple interest is calculated only on the original principal, so it grows linearly: $10,000 at 5% earns $500 every year indefinitely. Compound interest is calculated on principal plus accrued interest, so it grows exponentially. Over 30 years at 5%, simple interest turns $10,000 into $25,000, while annual compounding turns it into $43,219. Q: How does compounding frequency change the result? A: More frequent compounding produces a higher effective yield from the same nominal rate. $10,000 at 12% for one year grows to $11,200 with annual compounding, $11,268 with monthly compounding and $11,275 with daily compounding. The gain shrinks with each step up in frequency, converging on the continuous limit Pe^(rt), which gives $11,275. Q: What is the rule of 72? A: The rule of 72 estimates how long an investment takes to double: divide 72 by the annual percentage rate. At 8%, doubling takes roughly 72 ÷ 8 = 9 years, against an exact figure of 9.01 years. The approximation is accurate to within a few months for rates between about 4% and 15%. Q: What is APY and how does it differ from the interest rate? A: The annual percentage yield expresses what a nominal rate actually earns once compounding is accounted for, using APY = (1 + r/n)ⁿ − 1. A 12% nominal rate compounded monthly has an APY of 12.68%. In the United States, Regulation DD requires deposit accounts to advertise APY specifically so that accounts with different compounding schedules compare directly. Q: Does this calculator account for inflation, tax or fees? A: No. The result is a nominal, pre-tax, pre-fee figure. To approximate real purchasing power, subtract expected inflation from the return rate before entering it — a 7% return with 3% inflation is roughly a 4% real rate. Investment fees should be deducted from the rate in the same way. Q: Is a 7% annual return a reasonable assumption? A: Seven percent is a commonly used long-run estimate for a diversified equity portfolio after inflation, derived from roughly a century of US market history. It is an average across decades, not a guarantee for any single year — equity markets routinely deliver returns between −40% and +40% annually. Cash and bond assumptions should be considerably lower. Sources: - Compound interest — investor education and calculator — US Securities and Exchange Commission — https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator - Regulation DD — Truth in Savings and APY — US Consumer Financial Protection Bureau — https://www.consumerfinance.gov/rules-policy/regulations/1030/ - Saving and investing — a roadmap — US Securities and Exchange Commission — https://www.sec.gov/investor/pubs/sec-guide-to-savings-and-investing.pdf --- ### Savings goal calculator URL: https://truescalers.com/calculators/savings-goal-calculator Last reviewed: 2026-08-09 A savings goal calculator finds the monthly deposit required to reach a target by a chosen date, solving the annuity formula for the payment: PMT = (FV − P(1+r)ⁿ) × r ÷ ((1+r)ⁿ − 1). Reaching $50,000 in 5 years from $5,000 saved, at 4% interest, requires depositing $661.34 every month. Formula: PMT = (FV − P(1 + r)ⁿ) × r ÷ ((1 + r)ⁿ − 1) PMT = The deposit required at the end of each month. FV = The savings target — the future value you want to reach. P = The balance already saved today. r = The monthly interest rate: the annual rate divided by 100, then by 12. n = The number of monthly deposits, equal to the years multiplied by 12. Worked example — Savings goal: $50,000, Already saved: $5,000, Annual interest rate: 4%, Timeframe: 5 years → $661.34 per month The monthly rate r is 4 ÷ 100 ÷ 12 = 0.00333333, and n is 60 months. The existing $5,000 grows on its own to 5,000 × (1.00333333)^60 = $6,104.98. The shortfall the deposits must cover is $50,000 − $6,104.98 = $43,895.02. Solving the annuity formula: PMT = 43,895.02 × 0.00333333 ÷ ((1.00333333)^60 − 1) = 43,895.02 × 0.00333333 ÷ 0.220997 = $661.34. Total deposited across 60 months is $39,680, and interest supplies the remaining $5,320. Questions answered on this page: Q: How much should an emergency fund hold? A: The common guidance is three to six months of essential expenses, held in an instant-access account. Households with variable income, a single earner, or specialised employment usually target the upper end or beyond. The figure that matters is essential outgoings — housing, food, utilities, insurance, minimum debt payments — not total spending. Q: Does the interest rate matter much over short periods? A: Less than most savers expect. Reaching $50,000 in five years from $5,000 requires $661.34 a month at 4% and $698.42 a month at 1%. The difference is $37 a month, or 5.6%. Over longer horizons the rate dominates: across 25 years, compounding contributes more to the balance than the deposits do. Q: Should savings go into a high-yield savings account or investments? A: Horizon determines the answer. Money needed within five years generally belongs in a high-yield savings account, money-market fund or certificate of deposit, where the balance is not at risk. Money not needed for a decade or more has historically fared better in diversified equities, which are volatile year to year but higher-returning across decades. Q: Are savings deposits protected if the bank fails? A: In the United States, the FDIC insures deposits up to $250,000 per depositor, per insured bank, per ownership category; the NCUA provides equivalent cover at credit unions. In the United Kingdom, the FSCS covers £85,000 per person per authorised firm. Balances above those limits are best spread across separate institutions. Q: What does paying yourself first mean? A: Paying yourself first means scheduling an automatic transfer to savings on payday, before discretionary spending. Automation removes the monthly decision, which is where saving plans usually fail. Setting the standing order for the day after payday, rather than the end of the month, is measurably more effective at keeping the deposit intact. Q: Does this calculator account for tax on interest? A: No. Results are pre-tax. Interest earned in an ordinary savings account is generally taxable as income in the year received. To approximate the after-tax outcome, reduce the entered rate by your marginal tax rate — a 4% rate for a saver in a 24% bracket behaves like roughly 3.04%. Sources: - Deposit insurance coverage limits — US Federal Deposit Insurance Corporation — https://www.fdic.gov/resources/deposit-insurance/ - Saving for emergencies — US Consumer Financial Protection Bureau — https://www.consumerfinance.gov/consumer-tools/save-for-an-emergency/ - Compound interest and future value — US Securities and Exchange Commission — https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator --- ### Tip calculator URL: https://truescalers.com/calculators/tip-calculator Last reviewed: 2026-08-09 A tip calculator finds the gratuity on a bill and divides the total between diners. The tip is bill × (percentage ÷ 100), and each share is (bill + tip) ÷ number of people. An $85.50 bill with an 18% tip comes to $100.89 in total, which is $25.22 each when split four ways. Formula: tip = bill × (p ÷ 100); total = bill + tip; share = total ÷ people bill = The pre-tip amount shown on the check. p = The tip percentage. tip = The gratuity amount. total = The bill plus the tip. people = The number of diners the total is divided between. share = What each person pays. Worked example — Bill amount: $85.50, Tip percentage: 18%, Split between: 4 people → $25.22 each Convert the tip percentage to a multiplier: 18 ÷ 100 = 0.18. The tip is 85.50 × 0.18 = $15.39. The total is 85.50 + 15.39 = $100.89. Dividing between four diners gives 100.89 ÷ 4 = $25.22 each, of which $3.85 is the tip. Enabling round-up raises each share to $26.00, bringing the party total to $104.00 and the effective tip to 21.6%. Questions answered on this page: Q: How much should you tip at a restaurant in the United States? A: Fifteen percent of the pre-tax subtotal is the customary minimum for sit-down table service, eighteen to twenty percent is standard for good service, and twenty-five percent recognises exceptional service. Counter service, coffee shops and takeaway carry no obligation, although a small tip is common. Many US servers are paid a subminimum cash wage and depend on gratuities for most of their income. Q: Should you tip on the pre-tax or post-tax amount? A: US etiquette guidance is to tip on the pre-tax subtotal, because sales tax is remitted to the state and is not part of the service provided. Tipping on the post-tax total is nonetheless widespread and adds roughly the local tax rate to the effective gratuity — around 1.5 percentage points at an 8% tax rate. Q: How do you calculate a 20% tip quickly in your head? A: Move the decimal point one place left to find 10%, then double it. On an $85.50 bill, 10% is $8.55, so 20% is $17.10. For 15%, take the 10% figure and add half of it: $8.55 plus $4.28 is $12.83. For 18%, subtract a tenth from the 20% figure: $17.10 minus $1.71 is $15.39. Q: What is a gratuity or service charge added by the restaurant? A: A service charge is a mandatory amount added by the establishment, typically 18 to 20% for parties of six or more. It is legally the restaurant's revenue rather than a tip, and it may not reach the server in full. When a service charge already appears on the check, no additional tip is expected. Q: Do tipping customs differ outside the United States? A: Considerably. Japan treats tipping as inappropriate. Most of continental Europe includes service in the listed price and rounds up only for notable service, usually 5 to 10%. The United Kingdom and Australia sit near 10%, often only for table service. The US expectation of 18 to 20% is unusually high by international standards. Q: How do you split a bill fairly when orders differ in price? A: Splitting evenly is fastest and is appropriate when orders are broadly comparable. When one diner had a considerably more expensive meal, calculating each person's share of the subtotal and applying the same tip percentage to each is fairer. Whichever method is used, agreeing it before the check arrives avoids friction at the table. Sources: - Tipped employees — federal wage requirements — US Department of Labor — https://www.dol.gov/agencies/whd/fact-sheets/15-flsa-tipped-employees - Tip income reporting requirements — US Internal Revenue Service — https://www.irs.gov/taxtopics/tc761 - Service charges versus tips — US Department of Labor — https://www.dol.gov/agencies/whd/flsa/tips --- ### Discount calculator URL: https://truescalers.com/calculators/discount-calculator Last reviewed: 2026-08-09 A discount calculator finds a sale price from an original price and a percentage off, using sale = price × (1 − d ÷ 100). A $120 item with 25% off costs $90 and saves $30. Stacked discounts multiply rather than add, so 25% off followed by a further 10% off gives an effective discount of 32.5%, not 35%. Formula: sale = price × (1 − d₁ ÷ 100) × (1 − d₂ ÷ 100); saved = price − sale price = The original list price before any reduction. d₁ = The first discount percentage. d₂ = Any additional discount applied to the already-reduced price. sale = The price after all discounts. saved = The total reduction in currency terms. Worked example — Original price: $120, Discount: 25%, Extra discount: 10%, Sales tax: 0% → $81.00 The first discount leaves 1 − 0.25 = 0.75 of the price: 120 × 0.75 = $90.00, saving $30. The extra 10% applies to $90, not to $120: 90 × 0.90 = $81.00, saving a further $9. Total saved is $39, so the effective discount is 39 ÷ 120 = 32.5%, not the 35% that adding the two percentages would suggest. Questions answered on this page: Q: How do you calculate a percentage discount? A: Multiply the original price by the discount percentage divided by 100 to find the saving, then subtract it from the price. For 25% off $120, the saving is 120 × 0.25 = $30 and the sale price is $90. Equivalently, multiply the price directly by (1 − 0.25) to reach $90 in one step. Q: Do stacked discounts add together? A: No. Sequential discounts multiply, because each one applies to the price that remains after the previous reduction. Twenty-five percent off followed by 10% off leaves 0.75 × 0.90 = 0.675 of the original, an effective discount of 32.5%. Adding the percentages would overstate the saving by 2.5 percentage points. Q: What does buy one get one free work out to as a percentage? A: Buy one get one free is a 50% discount, provided both items are wanted. Buy one get one half price is a 25% discount across the pair. Buy two get one free is a 33.3% discount across the three. Each figure assumes every included item would have been purchased anyway at full price. Q: How do you find the original price from a sale price? A: Divide the sale price by one minus the discount as a decimal. An item selling for $81 after 32.5% off originally cost 81 ÷ (1 − 0.325) = 81 ÷ 0.675 = $120. This reverse calculation is the practical way to check whether an advertised "was" price is genuine. Q: Is sales tax charged on the original price or the discounted price? A: Sales tax is charged on the discounted price the customer actually pays, in every US state that levies it. A $120 item at 25% off sells for $90, and 8% tax adds $7.20 for a total of $97.20 — not the $9.60 that taxing the $120 list price would produce. Manufacturer coupons are the exception in some states, where tax may apply pre-coupon. Q: What is a percentage-off versus a fixed-amount coupon worth more? A: The basket value decides it. A 20% discount beats a flat $10 off whenever the price exceeds $50, and loses below it. The break-even point is the fixed amount divided by the percentage as a decimal: $10 ÷ 0.20 = $50. Checking that threshold settles which coupon to use when only one may be applied. Sources: - Guides against deceptive pricing — US Federal Trade Commission — https://www.ecfr.gov/current/title-16/chapter-I/subchapter-B/part-233 - Sales tax on discounted goods and coupons — Federation of Tax Administrators — https://www.taxadmin.org/ - Percentage arithmetic — standards reference — Common Core State Standards Initiative — https://www.thecorestandards.org/Math/Content/RP/ --- ### Sales tax calculator URL: https://truescalers.com/calculators/sales-tax-calculator Last reviewed: 2026-08-09 A sales tax calculator adds tax to a net price using gross = net × (1 + rate ÷ 100), or removes tax already included using net = gross ÷ (1 + rate ÷ 100). At a 7.25% rate, $200 before tax becomes $214.50, and a $214.50 tax-inclusive total contains $14.50 of tax on a $200 net price. Formula: gross = net × (1 + rate ÷ 100); net = gross ÷ (1 + rate ÷ 100) net = The price before tax. gross = The price including tax. rate = The combined tax rate as a percentage. tax = The tax amount, equal to gross minus net. Worked example — Amount: $200.00, Sales tax rate: 7.25%, Direction: Add tax to a pre-tax price → $214.50 Convert the rate into a multiplier: 1 + 7.25 ÷ 100 = 1.0725. Multiply the net price: 200 × 1.0725 = $214.50, of which $14.50 is tax. Reversing the calculation confirms it: 214.50 ÷ 1.0725 = $200.00 exactly. Subtracting 7.25% of $214.50 instead would give $198.95, understating the net price by $1.05. Questions answered on this page: Q: How do you calculate sales tax on a purchase? A: Multiply the pre-tax price by the tax rate expressed as a decimal, then add the result to the price. At a 7.25% rate, a $200 purchase carries 200 × 0.0725 = $14.50 of tax for a $214.50 total. Equivalently, multiply the price by 1.0725 to reach the total in a single step. Q: How do you work out the tax included in a total price? A: Divide the tax-inclusive total by one plus the rate as a decimal to recover the net price, then subtract. A $214.50 total at 7.25% divides to 214.50 ÷ 1.0725 = $200.00 net, leaving $14.50 of tax. Subtracting the percentage directly from the total is a common error and understates the net figure. Q: Which US state has the highest sales tax? A: California levies the highest statewide base rate at 7.25%, though combined state and local rates reach beyond 10% in parts of Louisiana, Tennessee, Arkansas, Washington and Alabama. Five states — Alaska, Delaware, Montana, New Hampshire and Oregon — impose no statewide sales tax, although Alaska permits local sales taxes. Q: What is the difference between sales tax and VAT? A: Sales tax is levied once, at the final retail sale, and is typically shown separately at the register. Value-added tax is collected at every stage of production, with each business reclaiming the tax it paid on inputs. VAT is normally included in the displayed shelf price, which is why European price tags rarely change at checkout. Q: Is sales tax charged on shipping? A: Treatment varies by state. Roughly half of US states tax delivery charges when the goods themselves are taxable; others exempt shipping when it is stated separately on the invoice. Because the rule follows the destination state in most remote-sales situations, sellers shipping across state lines must apply each destination's treatment. Q: Do online purchases carry sales tax? A: Generally yes, in the United States. The Supreme Court decision in South Dakota v. Wayfair (2018) allowed states to require sales tax collection from remote sellers exceeding an economic-nexus threshold, commonly $100,000 in sales or 200 transactions per year. Most large online retailers now collect tax at the buyer's destination rate. Sources: - South Dakota v. Wayfair, Inc., 585 U.S. 162 (2018) — Supreme Court of the United States — https://www.supremecourt.gov/opinions/17pdf/17-494_j4el.pdf - State sales tax rate tables — Federation of Tax Administrators — https://www.taxadmin.org/sales-tax-rates - VAT rates applied in EU member states — European Commission — https://taxation-customs.ec.europa.eu/taxation/vat/vat-rates_en --- ### BMI calculator URL: https://truescalers.com/calculators/bmi-calculator Last reviewed: 2026-08-09 Body mass index is body weight in kilograms divided by height in metres squared. An adult weighing 70 kg at 1.75 m has a BMI of 22.9, which the World Health Organization classifies as a healthy weight. The WHO adult bands are underweight below 18.5, healthy 18.5 to 24.9, overweight 25 to 29.9, and obese at 30 and above. Formula: BMI = weight(kg) ÷ height(m)² BMI = 703 × weight(lb) ÷ height(in)² 703 = The conversion constant that makes the imperial formula produce the same kg/m² value. BMI = Body mass index, expressed in kg/m². weight(kg) = Body mass in kilograms. height(m) = Standing height in metres. Worked example — Units: Metric, Weight: 70 kg, Height: 175 cm → BMI 22.9 — healthy weight Convert height to metres: 175 cm ÷ 100 = 1.75 m. Square it: 1.75 × 1.75 = 3.0625 m². Divide weight by that figure: 70 ÷ 3.0625 = 22.9 kg/m². That value falls inside the WHO healthy band of 18.5 to 24.9. For this height, the healthy band corresponds to a weight range of 56.7 kg to 76.3 kg, or 125 lb to 168 lb. Questions answered on this page: Q: What is a healthy BMI range for adults? A: The World Health Organization defines the healthy adult range as a BMI of 18.5 to 24.9 kg/m². Below 18.5 is classified as underweight, 25.0 to 29.9 as overweight, and 30.0 and above as obese, subdivided into class I at 30 to 34.9, class II at 35 to 39.9, and class III at 40 and above. Q: Is BMI accurate for muscular people? A: No. BMI measures total mass against height and cannot distinguish muscle from fat. Muscle is denser than fat, so trained athletes frequently register as overweight or obese despite low body fat. For anyone carrying substantial muscle, a waist-to-height ratio or a body fat estimate gives a far more informative picture. Q: Does BMI work for children and teenagers? A: Not with adult cut-offs. Children's body composition changes continuously with age, so paediatric assessment uses BMI-for-age percentiles from CDC or WHO growth charts rather than fixed thresholds. A child at or above the 95th percentile for their age and sex is classified as obese; between the 85th and 95th, overweight. Q: Do BMI thresholds differ by ethnicity? A: Yes. Cardiometabolic risk rises at lower BMI values in people of South Asian, Chinese and some other Asian ancestries. The WHO expert consultation identified 23 kg/m² as a public-health action point and 27.5 kg/m² as a high-risk threshold for these populations, and several national guidelines including NICE in the United Kingdom apply lowered cut-offs. Q: What is the healthy weight range for a given height? A: Multiply the height in metres squared by 18.5 and by 24.9 to obtain the lower and upper bounds. At 1.75 m, height squared is 3.0625, so the healthy range runs from 18.5 × 3.0625 = 56.7 kg to 24.9 × 3.0625 = 76.3 kg — approximately 125 lb to 168 lb. Q: What is a better measure of health risk than BMI? A: Waist circumference and waist-to-height ratio track abdominal fat, which drives cardiometabolic risk more directly than total mass. Keeping waist circumference below half of height is a widely used rule. Body fat percentage from a DEXA scan or bioelectrical impedance adds composition detail that BMI structurally cannot capture. Q: Is BMI valid during pregnancy? A: No. BMI is not a valid measure during pregnancy, because gestational weight gain reflects the fetus, placenta, amniotic fluid and expanded blood volume rather than body composition. Clinical guidance instead uses pre-pregnancy BMI to set recommended gestational weight gain ranges, which are monitored by an obstetric provider. Sources: - Obesity and overweight — BMI classification — World Health Organization — https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight - About Adult BMI — US Centers for Disease Control and Prevention — https://www.cdc.gov/bmi/adult-calculator/index.html - Appropriate body-mass index for Asian populations — WHO Expert Consultation, The Lancet — https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(03)15268-3/fulltext --- ### Calorie calculator URL: https://truescalers.com/calculators/calorie-calculator Last reviewed: 2026-08-09 A calorie calculator estimates daily energy needs from the Mifflin-St Jeor equation, which sets basal metabolic rate at 10 × weight(kg) + 6.25 × height(cm) − 5 × age + 5 for men and − 161 for women, then multiplies by an activity factor. A 30-year-old man of 70 kg and 175 cm has a BMR of 1,649 kcal and needs about 2,556 kcal a day at moderate activity. Formula: BMR = 10w + 6.25h − 5a + k TDEE = BMR × activity factor BMR = Basal metabolic rate in kilocalories per day — energy used at complete rest. w = Body weight in kilograms. h = Height in centimetres. a = Age in years. k = A sex constant: +5 for men, −161 for women. TDEE = Total daily energy expenditure, including all activity. activity factor = From 1.20 for sedentary to 1.90 for twice-daily training or heavy physical work. Worked example — Units: Metric, Weight: 70 kg, Height: 175 cm, Age: 30, Sex: Male, Activity level: Moderate (×1.55) → 2,556 kcal per day to maintain weight Apply the male Mifflin-St Jeor equation: (10 × 70) + (6.25 × 175) − (5 × 30) + 5 = 700 + 1,093.75 − 150 + 5 = 1,648.75 kcal, rounding to 1,649 kcal of basal metabolic rate. Multiply by the moderate activity factor: 1,648.75 × 1.55 = 2,555.6 kcal per day for maintenance. A 500 kcal daily deficit gives roughly 2,056 kcal, which produces about 0.45 kg (1 lb) of loss per week, since a kilogram of body fat stores roughly 7,700 kcal. Questions answered on this page: Q: How many calories should I eat a day to lose weight? A: A deficit of 500 kilocalories a day below maintenance produces roughly 0.45 kg (1 lb) of loss per week, because a kilogram of body fat stores approximately 7,700 kilocalories. Deficits above 1,000 kcal per day risk muscle loss and nutrient shortfall. Intake below 1,200 kcal for women or 1,500 kcal for men warrants medical supervision. Q: What is the difference between BMR and TDEE? A: Basal metabolic rate is the energy the body uses at complete rest to sustain circulation, respiration, temperature and cell function — typically 60 to 70% of daily expenditure. Total daily energy expenditure adds the thermic effect of food, deliberate exercise, and non-exercise movement. TDEE is BMR multiplied by an activity factor between 1.20 and 1.90. Q: How accurate is the Mifflin-St Jeor equation? A: Mifflin-St Jeor predicts measured resting energy expenditure within 10% for roughly 80% of non-obese adults, which makes it the most accurate of the widely used predictive equations. Individual variation of ±10% remains, so the figure is a starting estimate. Two to three weeks of tracked weight change is a more reliable guide than any equation. Q: Which activity multiplier should I choose? A: Use 1.20 for a desk job with no deliberate exercise, 1.375 for light exercise one to three days a week, 1.55 for moderate exercise three to five days, 1.725 for hard exercise six or seven days, and 1.90 for a physically demanding job or twice-daily training. Self-reported activity is routinely overstated, so choose conservatively. Q: Do calorie needs fall with age? A: Yes. The Mifflin-St Jeor equation subtracts 5 kilocalories per year of age, so a 60-year-old needs about 150 kcal per day less than a 30-year-old of identical size. Most of the real-world decline comes from lost muscle mass and reduced spontaneous movement rather than from age itself, which is why resistance training substantially blunts it. Q: Does a calorie deficit still work if metabolism adapts? A: Metabolic adaptation is real but modest. Sustained restriction lowers energy expenditure by roughly 10 to 15% beyond what the smaller body size predicts, through reduced non-exercise movement and hormonal change. Energy balance still governs the outcome; the practical implication is that maintenance intake must be recalculated as weight falls. Q: How many calories are in a kilogram of body fat? A: Approximately 7,700 kilocalories per kilogram, or 3,500 per pound. The figure comes from adipose tissue being about 87% lipid, with each gram of fat supplying 9 kilocalories. Early weight change is faster than this predicts because glycogen and its bound water are lost first, which is why the first fortnight tends to flatter a new deficit. Sources: - A new predictive equation for resting energy expenditure in healthy individuals — Mifflin et al., American Journal of Clinical Nutrition, 1990 — https://pubmed.ncbi.nlm.nih.gov/2305711/ - Dietary Guidelines for Americans — estimated calorie needs — US Departments of Agriculture and Health and Human Services — https://www.dietaryguidelines.gov/ - Healthy diet — energy intake fact sheet — World Health Organization — https://www.who.int/news-room/fact-sheets/detail/healthy-diet --- ### Body fat calculator URL: https://truescalers.com/calculators/body-fat-calculator Last reviewed: 2026-08-09 The US Navy circumference method estimates body fat percentage from height, neck and waist measurements, adding hip circumference for women. A man of 180 cm with a 38 cm neck and 85 cm waist has an estimated 16.7% body fat, which falls in the fitness range. The method agrees with hydrostatic weighing to within about three percentage points. Formula: men: 495 ÷ (1.0324 − 0.19077·log₁₀(waist − neck) + 0.15456·log₁₀(height)) − 450 | women: 495 ÷ (1.29579 − 0.35004·log₁₀(waist + hip − neck) + 0.22100·log₁₀(height)) − 450 waist = Waist circumference in centimetres — at the navel for men, at the narrowest point for women. neck = Neck circumference in centimetres, measured just below the larynx. hip = Hip circumference in centimetres at the widest point. Used in the female formula only. height = Standing height in centimetres. log₁₀ = The base-10 logarithm. Worked example — Sex: Male, Height: 180 cm, Neck: 38 cm, Waist: 85 cm, Weight: 80 kg → 16.7% body fat — fitness range Subtract neck from waist: 85 − 38 = 47 cm. Take base-10 logarithms: log₁₀(47) = 1.67210 and log₁₀(180) = 2.25527. Substitute into the male equation: the denominator is 1.0324 − (0.19077 × 1.67210) + (0.15456 × 2.25527) = 1.0324 − 0.31899 + 0.34857 = 1.06198. Then 495 ÷ 1.06198 = 466.15, and subtracting 450 gives 16.7% body fat. At 80 kg that is 13.3 kg of fat mass and 66.7 kg of lean mass. Questions answered on this page: Q: What is a healthy body fat percentage? A: The American Council on Exercise places men at 6 to 13% for athletes, 14 to 17% for fitness, 18 to 24% as average, and 25% or above as obese. For women the corresponding bands are 14 to 20%, 21 to 24%, 25 to 31%, and 32% or above. Women carry more essential fat for hormonal and reproductive function, which is why every band sits higher. Q: How accurate is the US Navy body fat formula? A: The Navy circumference method agrees with hydrostatic weighing to within roughly ±3 percentage points for most adults. Accuracy declines at the extremes of body composition and for people whose fat distribution is unusual for their sex. Measurement technique is the largest source of error: a tape pulled tight or placed a few centimetres off shifts the result noticeably. Q: What is the most accurate way to measure body fat? A: A four-compartment model combining hydrostatic weighing, deuterium dilution and DEXA is the research reference standard. In clinical practice, DEXA is the accepted benchmark, accurate to within 1 to 2 percentage points. Air-displacement plethysmography sits close behind. Bioelectrical impedance scales are the least reliable, being sensitive to hydration, recent meals and exercise. Q: Why does body fat matter more than weight? A: Body weight combines fat, muscle, bone, organs and water, and cannot distinguish between them. Two adults of identical height and weight can differ by twenty percentage points of body fat. Health risk tracks fat mass and its distribution, particularly visceral fat around the organs, rather than total mass — which is exactly what BMI cannot see. Q: What is essential body fat? A: Essential fat is the minimum required for normal physiological function, including nerve insulation, organ protection and hormone production. It is roughly 3 to 5% of body mass in men and 10 to 13% in women. Sustained levels below these thresholds impair immune function, bone density and reproductive hormone production. Q: Can body fat percentage change quickly? A: Genuine change is slow, at roughly 0.5 to 1 percentage point per fortnight under a well-managed deficit. Larger day-to-day swings in any estimate reflect hydration, glycogen storage, food volume and measurement variation rather than tissue change. Measuring under identical conditions — same time of day, same tape, before eating — is what makes a trend interpretable. Sources: - Prediction of percent body fat for U.S. Navy men and women from body circumferences and height — Hodgdon and Beckett, Naval Health Research Center, 1984 — https://apps.dtic.mil/sti/citations/ADA143890 - Percent body fat norms for men and women — American Council on Exercise — https://www.acefitness.org/resources/everyone/tools-calculators/percent-body-fat-calculator/ - Body composition measurement methods — US National Institute of Diabetes and Digestive and Kidney Diseases — https://www.niddk.nih.gov/health-information/weight-management --- ### Age calculator URL: https://truescalers.com/calculators/age-calculator Last reviewed: 2026-08-09 An age calculator counts the whole years, then whole months, then remaining days between a date of birth and a chosen date. Someone born on 15 May 1990 is 36 years, 2 months and 25 days old on 9 August 2026, which is 13,235 days in total. The next birthday falls 279 days later, on 15 May 2027. Formula: age = whole years elapsed, then whole months, then remaining days whole years = Complete anniversaries of the birth date that have already passed. whole months = Complete calendar months since the most recent birthday. remaining days = Days since the last whole month boundary, clamped to real month lengths. total days = The exact count of calendar days between the two dates, including leap days. Worked example — Date of birth: 15 May 1990, Age at this date: 9 August 2026 → 36 years, 2 months and 25 days From 15 May 1990 to 15 May 2026 is 36 complete years. From 15 May 2026 to 15 July 2026 is a further 2 complete months, reaching 15 July 2026. From 15 July 2026 to 9 August 2026 is 25 remaining days. The total elapsed period is 13,235 days, which includes 9 leap days. The next birthday, 15 May 2027, is 279 days after the comparison date. Questions answered on this page: Q: How is exact age calculated? A: Exact age counts complete years from the birth date first, then complete months from the most recent birthday, then the remaining days. This ordering matters: counting total days and dividing by 365.25 gives a decimal approximation, not the calendar age used for legal, medical and administrative purposes. Q: How is age handled for someone born on 29 February? A: A leap-day birth date has no anniversary in common years, so a convention is required. The prevailing legal and administrative treatment in the United States and the United Kingdom recognises 1 March in common years, and this calculator follows that convention. Some jurisdictions and organisations instead use 28 February. Q: How many days are there in an average year? A: The Gregorian calendar averages 365.2425 days per year. Leap years add a day in every year divisible by four, except centuries not divisible by four hundred — so 1900 was not a leap year and 2000 was. That rule keeps the calendar aligned with the solar year to within one day per 3,030 years. Q: How do you calculate age in months? A: Multiply the whole years by twelve and add the whole months. Someone 36 years and 2 months old has lived 36 × 12 + 2 = 434 complete months. Paediatric growth charts and vaccination schedules use age in whole months for the first several years, because monthly resolution matters most when development is fastest. Q: Does this age calculator work for future dates? A: Yes. Setting the comparison date in the future returns the age that will be reached on that date. This is the practical way to check school entry cut-offs, retirement dates, licence eligibility, or minimum age requirements for a scheduled event. The comparison date must fall on or after the birth date. Q: Why does my age differ by a day in some calculators? A: Time-zone handling is the usual cause. A calculator using local time can advance or delay the date boundary by up to a day relative to one using UTC. This calculator performs all arithmetic in UTC, treating a birth date as a calendar fact rather than an instant, so the same inputs always produce the same result anywhere in the world. Sources: - Leap years and the Gregorian calendar — US National Institute of Standards and Technology — https://www.nist.gov/pml/time-and-frequency-division/popular-links/time-frequency-z/time-and-frequency-z-l - ISO 8601 — date and time representation — International Organization for Standardization — https://www.iso.org/iso-8601-date-and-time-format.html - Leap seconds and calendar timekeeping — US Naval Observatory — https://www.usno.navy.mil/USNO/astronomical-applications --- ### Date duration calculator URL: https://truescalers.com/calculators/date-duration-calculator Last reviewed: 2026-08-09 A date duration calculator counts the calendar days between two dates and splits them into weekdays and weekend days. Between 1 January 2026 and 25 December 2026 there are 358 days, of which 256 are weekdays and 102 fall on a Saturday or Sunday. That period equals 11 months and 24 days, or 51 whole weeks. Formula: days = (end − start) ÷ 86,400,000 ms, computed in UTC start = The earlier calendar date. end = The later calendar date. days = Whole calendar days between the two, counting the start day as day zero. 86,400,000 = Milliseconds in a day: 24 × 60 × 60 × 1,000. Worked example — Start date: 1 January 2026, End date: 25 December 2026 → 358 days The interval spans 358 calendar days. Dividing by seven gives 51 complete weeks with a remainder of 1 day. Each complete week contributes exactly 5 weekdays, giving 255, and the single remaining day is examined individually and is a weekday, bringing the total to 256 weekdays and 102 weekend days. Expressed as a calendar period the interval is 11 months and 24 days, and as hours it is 8,592. Questions answered on this page: Q: How do you count the days between two dates? A: Subtract the earlier date from the later one and divide by the number of milliseconds in a day. The result counts the start day as day zero, so 1 January to 2 January is one day. Counting both endpoints — an inclusive count — adds one, which is the convention used for hotel nights and hire periods. Q: What is the difference between calendar days and business days? A: Calendar days count every day including weekends and public holidays. Business days count only Monday to Friday, and formal definitions usually also exclude public holidays. Contracts, court deadlines and shipping estimates frequently specify business days, so a 10-business-day period spans at least 14 calendar days. Q: Why does adding months give a different answer than adding days? A: Months have unequal lengths, so month arithmetic is not fixed-length arithmetic. Three months from 31 January lands on 30 April, since no 31 April exists — but 90 days from 31 January lands on 1 May in a common year. Legal periods expressed in months follow the calendar convention, not the day count. Q: How many working days are there in a year? A: A common year contains 261 or 262 weekdays depending on which day of the week it begins; a leap year contains 262 or 263. Subtracting public holidays gives the practical figure: about 250 in the United States with 11 federal holidays, and about 253 in the United Kingdom with 8 bank holidays in England and Wales. Q: Does this calculator account for daylight saving time? A: Daylight saving has no effect on the result. All arithmetic runs in Coordinated Universal Time, which has no daylight-saving transitions. Calculating in local time would make two days a year 23 and 25 hours long, and a naive division by 24 hours would then produce off-by-one errors across any span containing a clock change. Q: How do you calculate a deadline a set number of days away? A: Add the period to the start date, then check whether the result falls on a weekend or public holiday. Most legal and administrative rules roll a deadline landing on a non-working day forward to the next working day. Where the rule specifies business days, count only Monday to Friday from the day after the triggering event. Sources: - ISO 8601 — date and time representation — International Organization for Standardization — https://www.iso.org/iso-8601-date-and-time-format.html - Federal holidays — US Office of Personnel Management — https://www.opm.gov/policy-data-oversight/pay-leave/federal-holidays/ - Coordinated Universal Time and civil timekeeping — US National Institute of Standards and Technology — https://www.nist.gov/pml/time-and-frequency-division --- ### Grade calculator URL: https://truescalers.com/calculators/grade-calculator Last reviewed: 2026-08-09 A grade calculator finds a weighted course average as G = Σ(scoreᵢ × weightᵢ) ÷ Σweightᵢ. Homework at 95% worth 20%, a midterm at 88% worth 30%, and a final at 92% worth 50% produce an overall grade of 91.4%, which is an A− on the standard US letter scale and 3.7 grade points on the 4.0 scale. Formula: G = Σ(scoreᵢ × weightᵢ) ÷ Σweightᵢ needed = (target − G × (1 − w)) ÷ w G = The overall weighted grade as a percentage. scoreᵢ = The percentage earned on assessment i. weightᵢ = The relative weight of assessment i. Only the ratio matters, so weights need not sum to 100. target = The overall grade you are aiming for. w = The share of the final grade still outstanding, as a decimal. needed = The score required on the remaining work to reach the target. Worked example — Assessments: Homework 95% (weight 20); Midterm 88% (weight 30); Final exam 92% (weight 50), Target grade: 90% → 91.40% — A− Multiply each score by its weight: 95 × 20 = 1,900, 88 × 30 = 2,640, and 92 × 50 = 4,600. Sum the products: 1,900 + 2,640 + 4,600 = 9,140. Sum the weights: 20 + 30 + 50 = 100. Divide: 9,140 ÷ 100 = 91.40%. On the standard US scale that is an A−, worth 3.7 grade points. The target of 90% is already exceeded, so no further score is required. Questions answered on this page: Q: How do you calculate a weighted grade? A: Multiply each score by its weight, add the products together, then divide by the sum of the weights. For scores of 95, 88 and 92 with weights of 20, 30 and 50, the products total 9,140 and the weights total 100, giving 91.40%. Averaging the three scores without weighting would give 91.67% — a different and incorrect answer. Q: What score do I need on the final exam? A: Use needed = (target − current × (1 − w)) ÷ w, where w is the final exam's share of the grade as a decimal. Holding 85% across 70% of the course and targeting 90% overall requires (90 − 85 × 0.7) ÷ 0.3 = 101.67% on the final — mathematically out of reach without extra credit. Q: What percentage is an A grade? A: On the most common US scale, an A is 93 to 96%, an A+ is 97% and above, and an A− is 90 to 92%. B grades run from 80 to 89%, C from 70 to 79%, D from 60 to 69%, and F below 60%. Institutions vary, so the registrar's published scale governs any official transcript. Q: Do weights have to add up to 100? A: No. Only the ratio between weights affects the result, so 2, 3 and 5 produce exactly the same average as 20, 30 and 50. Weights totalling less than 100 are useful mid-semester: the calculator treats the shortfall as outstanding and computes the score needed on it to reach a target. Q: How does dropping the lowest grade change the average? A: Remove that assessment's line entirely and recalculate. Both the numerator and the denominator shrink, so the effect is larger than it first appears — dropping a 40% from a set of 90s can lift an average by several points. Where a syllabus replaces a dropped score rather than removing it, enter the replacement instead. Q: What is the difference between a weighted and an unweighted grade? A: An unweighted average treats every assessment as equally important, which is only correct when every assessment carries the same weight. A weighted average scales each score by its stated share of the final grade. Since a final exam typically counts for far more than a single homework set, weighting is what makes the number meaningful. Sources: - Grading and academic standing policies — reference practice — US National Center for Education Statistics — https://nces.ed.gov/ - Weighted mean — definition and method — Encyclopædia Britannica — https://www.britannica.com/science/mean-mathematics - Ratios and proportional relationships — standards — Common Core State Standards Initiative — https://www.thecorestandards.org/Math/Content/RP/ --- ### GPA calculator URL: https://truescalers.com/calculators/gpa-calculator Last reviewed: 2026-08-09 Grade point average is the credit-weighted mean of grade points: GPA = Σ(pointsᵢ × creditsᵢ) ÷ Σcreditsᵢ. Five courses graded A, B+, A−, B and A across 17 credit hours produce 62.0 quality points and a GPA of 3.65 on the 4.0 scale. Credit hours, not course count, determine how much each grade matters. Formula: GPA = Σ(grade pointsᵢ × creditsᵢ) ÷ Σcreditsᵢ grade pointsᵢ = The 4.0-scale value of the letter grade: A = 4.0, A− = 3.7, B+ = 3.3, B = 3.0, and so on. creditsᵢ = The credit hours the course carries. quality points = The product of grade points and credits for a single course. GPA = Total quality points divided by total credit hours. Worked example — Courses: Biology A (4 cr); Calculus B+ (3 cr); English A− (3 cr); History B (3 cr); Chemistry A (4 cr), Previous GPA: 0 (this term only) → GPA 3.65 Convert each letter to grade points and multiply by credits: Biology 4.0 × 4 = 16.0, Calculus 3.3 × 3 = 9.9, English 3.7 × 3 = 11.1, History 3.0 × 3 = 9.0, Chemistry 4.0 × 4 = 16.0. Quality points total 62.0 and credits total 17. Dividing gives 62.0 ÷ 17 = 3.65. Note that Biology and Chemistry carry 4 credits each and therefore weigh more heavily than the 3-credit courses. Questions answered on this page: Q: How is GPA calculated? A: Multiply each course's grade points by its credit hours to get quality points, sum the quality points, and divide by the total credit hours. A 4-credit A contributes 16 quality points while a 3-credit A contributes 12, which is why credit-heavy courses move a GPA further than credit-light ones. Q: What grade points does each letter grade carry? A: On the standard US 4.0 scale, A and A+ are 4.0, A− is 3.7, B+ is 3.3, B is 3.0, B− is 2.7, C+ is 2.3, C is 2.0, C− is 1.7, D+ is 1.3, D is 1.0, D− is 0.7, and F is 0.0. Some institutions award 4.3 for an A+; most cap the scale at 4.0. Q: How do you calculate a cumulative GPA? A: Multiply the previous cumulative GPA by the credits it covers to recover prior quality points, add the new term's quality points, then divide by the combined credit total. A 3.50 GPA over 60 credits carries 210 quality points; adding a term of 62.0 points over 17 credits gives 272.0 ÷ 77 = 3.53. Q: What is the difference between weighted and unweighted GPA? A: An unweighted GPA caps every course at 4.0 regardless of difficulty. A weighted GPA, common in US high schools, adds a bonus for honours, Advanced Placement and International Baccalaureate courses — typically 0.5 or 1.0 point — which is why weighted GPAs can exceed 4.0 and reach 5.0. Q: Does a pass or fail grade affect GPA? A: Usually not. A pass grade normally awards the credit hours but no quality points, so it is excluded from the GPA calculation entirely. A fail in a pass/fail course is treated differently by different institutions: some exclude it, others record it as 0.0 grade points and include it. Check the registrar's policy before electing pass/fail. Q: How much can one bad grade lower a GPA? A: The effect shrinks as credits accumulate. A 3-credit F added to a 3.70 GPA over 15 credits drops it to 3.08. The same F added to a 3.70 GPA over 90 credits drops it only to 3.58. This is also why early coursework has an outsized and lasting influence on a final transcript. Q: Do retaken courses replace the original grade? A: Institutional policy decides. Grade replacement removes the original attempt from the GPA calculation and counts only the retake. Grade forgiveness policies often limit how many times replacement may be used. Where no replacement policy exists, both attempts remain in the calculation and the retake merely dilutes the original. Sources: - Postsecondary grading and credit-hour reporting — US National Center for Education Statistics — https://nces.ed.gov/ipeds/ - Credit hour — federal definition — US Department of Education — https://www.ecfr.gov/current/title-34/subtitle-A/part-600/section-600.2 - Weighted mean — definition and method — Encyclopædia Britannica — https://www.britannica.com/science/mean-mathematics --- ## Converters TrueScalers publishes six unit converters covering length, weight, temperature, speed, volume and digital storage. Conversion factors use the exact internationally agreed definitions — one inch is exactly 25.4 millimetres and one pound is exactly 0.45359237 kilograms — so results are exact rather than approximate. ### Length converter URL: https://truescalers.com/converters/length-converter Last reviewed: 2026-08-09 A length converter changes a distance from one unit to another by multiplying through a shared base unit. One inch is exactly 25.4 millimetres by international agreement, so 180 centimetres equals 70.8661 inches, or 5 feet 10.87 inches. One mile is exactly 1,609.344 metres, so 5 kilometres equals 3.106856 miles. Formula: result = value × (factor_from ÷ factor_to) value = The quantity being converted. factor_from = Metres per unit of the source unit — 0.0254 for the inch. factor_to = Metres per unit of the target unit. result = The equivalent quantity in the target unit. Worked example — Length: 180, From: Centimetres, To: Inches → 70.86614 inches Convert the source quantity to metres: 180 cm × 0.01 = 1.8 m. Divide by the metres-per-inch factor: 1.8 ÷ 0.0254 = 70.86614 inches. Expressed in feet and inches, 70.86614 ÷ 12 = 5 feet with a remainder of 10.87 inches. The reverse factor is exact by definition: one inch equals 2.54 centimetres precisely, not approximately. Questions answered on this page: Q: How many centimetres are in an inch? A: One inch is exactly 2.54 centimetres. This is a definition rather than a measurement: the 1959 international yard and pound agreement fixed the inch at exactly 25.4 millimetres, harmonising slightly different national standards that had existed until then. All inch-to-metric conversions are therefore exact. Q: How do you convert centimetres to feet and inches? A: Divide the centimetre value by 2.54 to obtain total inches, then divide by 12 for whole feet and keep the remainder as inches. For 180 cm: 180 ÷ 2.54 = 70.866 inches, and 70.866 ÷ 12 gives 5 feet with 10.87 inches remaining, so 180 cm is 5 ft 10.9 in. Q: How many kilometres are in a mile? A: One mile is exactly 1.609344 kilometres, and one kilometre is 0.621371 miles. A 5 km race is 3.107 miles, a 10 km race is 6.214 miles, and a marathon of 42.195 km is 26.219 miles. The mile derives from the Roman mille passus, a thousand paces of five feet each. Q: What is a nautical mile and why does it differ? A: A nautical mile is exactly 1,852 metres, or 1.15078 statute miles. It was defined as one minute of arc of latitude along a meridian, which makes chart navigation direct: one minute of latitude is one nautical mile anywhere on Earth. Speed in knots is nautical miles per hour, so 1 knot equals 1.852 km/h. Q: Why is the metre defined by the speed of light? A: Since 1983 the metre has been defined as the distance light travels in a vacuum in 1/299,792,458 of a second. Defining it against a physical constant rather than a platinum-iridium bar means any properly equipped laboratory can realise the standard independently, with far better precision and no risk of the artefact drifting or being damaged. Q: Which countries still use imperial length units? A: The United States, Liberia and Myanmar are the three countries that have not formally adopted the metric system for general use. The United Kingdom and Canada are officially metric but retain imperial units in specific contexts — road distances in miles, personal height in feet and inches, and beer in pints. Sources: - The International System of Units (SI Brochure) — Bureau International des Poids et Mesures — https://www.bipm.org/en/publications/si-brochure - International yard and pound agreement of 1959 — US National Institute of Standards and Technology — https://www.nist.gov/pml/us-surveyfoot - NIST Guide to the SI — conversion factors — US National Institute of Standards and Technology — https://www.nist.gov/pml/special-publication-811 --- ### Weight converter URL: https://truescalers.com/converters/weight-converter Last reviewed: 2026-08-09 A weight converter changes a mass from one unit to another through a shared base unit. One pound is exactly 0.45359237 kilograms by the 1959 international agreement, so 70 kilograms equals 154.3236 pounds, or 11 stone 0.3 pounds. One ounce is exactly 28.349523125 grams, and one stone is exactly 14 pounds. Formula: result = value × (factor_from ÷ factor_to) value = The mass being converted. factor_from = Kilograms per unit of the source unit — 0.45359237 for the pound. factor_to = Kilograms per unit of the target unit. result = The equivalent mass in the target unit. Worked example — Weight: 70, From: Kilograms, To: Pounds → 154.32358 pounds Divide the mass in kilograms by the kilograms-per-pound factor: 70 ÷ 0.45359237 = 154.32358 pounds. To express that in stone and pounds, divide by 14: 154.32358 ÷ 14 = 11 stone with a remainder of 0.32 pounds, so 70 kg is 11 st 0.3 lb. The reverse is exact: one pound is 0.45359237 kilograms precisely. Questions answered on this page: Q: How many pounds are in a kilogram? A: One kilogram is 2.20462262 pounds, and one pound is exactly 0.45359237 kilograms. The pound figure is a definition set by the 1959 international yard and pound agreement, not a measurement, so every kilogram-to-pound conversion is exact rather than approximate. For rough mental arithmetic, doubling and adding ten percent is accurate to within half a percent. Q: How do you convert kilograms to stone and pounds? A: Multiply the kilograms by 2.20462 to get total pounds, then divide by 14 for whole stone and keep the remainder in pounds. For 70 kg: 70 × 2.20462 = 154.32 lb, and 154.32 ÷ 14 gives 11 stone with 0.32 lb remaining. The stone remains in everyday use for body weight in the United Kingdom and Ireland. Q: What is the difference between a metric tonne, a US ton and a UK ton? A: A metric tonne is exactly 1,000 kilograms, about 2,204.6 pounds. A US short ton is 2,000 pounds, about 907.2 kilograms. A UK long ton is 2,240 pounds, about 1,016 kilograms. The three differ by up to twelve percent, so shipping and freight documents must state which is meant. Q: Why was the kilogram redefined in 2019? A: Until 2019 the kilogram was defined by a platinum-iridium cylinder held near Paris, and that artefact had drifted by roughly 50 micrograms relative to its official copies. The 2019 redefinition fixed the Planck constant at exactly 6.62607015 × 10⁻³⁴ joule-seconds, allowing the kilogram to be realised from physical constants in any suitably equipped laboratory. Q: What is the difference between a troy ounce and a regular ounce? A: A troy ounce is 31.1034768 grams and is used for precious metals. An avoirdupois ounce, the everyday ounce, is 28.349523125 grams. A troy ounce is therefore about 10% heavier. Gold and silver prices are always quoted per troy ounce, which is why converting a bullion weight with the everyday factor understates its value. Q: Is weight the same as mass? A: Not in physics. Mass is the amount of matter in an object and does not change with location. Weight is the force gravity exerts on that mass, measured in newtons, and varies with local gravity — an object weighs about one sixth as much on the Moon. Everyday usage treats the two as interchangeable because terrestrial gravity barely varies. Sources: - The International System of Units (SI Brochure) — Bureau International des Poids et Mesures — https://www.bipm.org/en/publications/si-brochure - Redefining the kilogram — US National Institute of Standards and Technology — https://www.nist.gov/si-redefinition/kilogram - NIST Handbook 44 — weights and measures — US National Institute of Standards and Technology — https://www.nist.gov/pml/owm/nist-handbook-44 --- ### Temperature converter URL: https://truescalers.com/converters/temperature-converter Last reviewed: 2026-08-09 Temperature conversion between Celsius and Fahrenheit uses °F = °C × 9/5 + 32, and the inverse °C = (°F − 32) × 5/9. Water freezes at 0 °C and 32 °F and boils at 100 °C and 212 °F at standard pressure. The two scales read the same value at −40 degrees, and normal human body temperature of 37 °C equals 98.6 °F. Formula: °F = °C × 9/5 + 32 °C = (°F − 32) × 5/9 K = °C + 273.15 °C = Degrees Celsius. Zero is the freezing point of water at standard pressure. °F = Degrees Fahrenheit. The scale places water's freezing point at 32 and its boiling point at 212. K = Kelvin — the SI base unit of thermodynamic temperature. Zero kelvin is absolute zero, and no degree symbol is used. 9/5 = The ratio of a Fahrenheit degree interval to a Celsius one: 180 Fahrenheit degrees span the same range as 100 Celsius degrees. Worked example — Temperature: 100, From: Celsius, To: Fahrenheit → 212 °F Multiply the Celsius value by the interval ratio: 100 × 9/5 = 180. Add the offset that aligns the two zero points: 180 + 32 = 212 °F, the boiling point of water at standard atmospheric pressure. The same reading is 373.15 K, found by adding 273.15 to the Celsius value, and 671.67 °R on the Rankine scale. Questions answered on this page: Q: How do you convert Celsius to Fahrenheit? A: Multiply the Celsius value by 9/5, which is 1.8, then add 32. For 20 °C: 20 × 1.8 = 36, and 36 + 32 = 68 °F. For a quick mental estimate, double the Celsius figure and add 30 — that gives 70 for 20 °C, within two degrees across the range of ordinary weather temperatures. Q: How do you convert Fahrenheit to Celsius? A: Subtract 32, then multiply by 5/9. For 98.6 °F: 98.6 − 32 = 66.6, and 66.6 × 5/9 = 37 °C. The subtraction must come first, because it aligns the two zero points before the interval scaling is applied. Reversing the order produces an error of roughly 18 degrees. Q: At what temperature do Celsius and Fahrenheit read the same? A: At −40 degrees. Setting the two scales equal gives x = 1.8x + 32, which solves to x = −40. It is the only point where the two agree, because the scales have different zero points and different interval sizes and therefore cross exactly once. Q: What is absolute zero? A: Absolute zero is the lowest possible thermodynamic temperature, at which particles retain only quantum-mechanical zero-point motion. It sits at 0 K, −273.15 °C and −459.67 °F. The third law of thermodynamics establishes that it cannot be reached in a finite number of steps; laboratories have come within a few hundred picokelvin. Q: Why does the Fahrenheit scale use 32 and 212? A: Daniel Gabriel Fahrenheit set zero at the temperature of a brine mixture of ice, water and ammonium chloride, and 96 at approximately human body temperature. Water's freezing and boiling points fell at 32 and 212 as a consequence. The scale was later redefined against those two water points, which shifted body temperature to 98.6. Q: When should Kelvin be used instead of Celsius? A: Kelvin is required whenever temperature appears in a physical law, because gas laws, blackbody radiation and thermodynamic efficiency all depend on absolute temperature. Doubling absolute temperature doubles the mean kinetic energy of particles; doubling a Celsius reading has no physical meaning at all. Q: How do you convert a temperature difference rather than a reading? A: Apply only the multiplier, never the offset. A difference of 10 °C is a difference of 18 °F, because 10 × 1.8 = 18 — the 32-degree offset would be wrong here, as it aligns zero points rather than scaling intervals. A difference of 1 °C is exactly a difference of 1 K, since the two scales share an interval size. Sources: - The kelvin — SI base unit definition — Bureau International des Poids et Mesures — https://www.bipm.org/en/measurement-units/si-base-units - ITS-90 international temperature scale — US National Institute of Standards and Technology — https://www.nist.gov/pml/weights-and-measures/si-units-temperature - Redefining the kelvin — US National Institute of Standards and Technology — https://www.nist.gov/si-redefinition/kelvin --- ### Speed converter URL: https://truescalers.com/converters/speed-converter Last reviewed: 2026-08-09 A speed converter changes a rate from one unit to another through metres per second as the base. One mile per hour is exactly 0.44704 metres per second, so 100 kilometres per hour equals 62.1371 miles per hour. One knot is exactly 1.852 kilometres per hour, because a nautical mile is defined as exactly 1,852 metres. Formula: result = value × (factor_from ÷ factor_to) value = The speed being converted. factor_from = Metres per second per unit of the source unit — 0.44704 for mph. factor_to = Metres per second per unit of the target unit. result = The equivalent speed in the target unit. Worked example — Speed: 100, From: Kilometres per hour, To: Miles per hour → 62.13712 mph Convert to the base unit first: 100 km/h ÷ 3.6 = 27.77778 m/s. Divide by the metres-per-second-per-mph factor: 27.77778 ÷ 0.44704 = 62.13712 mph. Both factors are exact by definition, so the conversion carries no approximation. The same speed is 53.9957 knots and 91.1344 feet per second. Questions answered on this page: Q: How do you convert km/h to mph? A: Multiply the kilometres-per-hour figure by 0.621371. A speed of 100 km/h is 62.14 mph, 50 km/h is 31.07 mph, and 120 km/h is 74.56 mph. For a quick mental estimate, multiply by six and drop the last digit — 100 becomes 600, then 60, which is within four percent of the exact answer. Q: What is a knot and why is it used at sea and in aviation? A: A knot is one nautical mile per hour, exactly 1.852 km/h or 1.15078 mph. Because a nautical mile equals one minute of latitude, a vessel travelling at 10 knots for one hour has moved exactly 10 minutes of latitude on the chart. That direct relationship to chart geometry is why marine and air navigation retain the unit. Q: How do you convert km/h to metres per second? A: Divide by exactly 3.6. An hour holds 3,600 seconds and a kilometre holds 1,000 metres, so the ratio is 3,600 ÷ 1,000 = 3.6. A speed of 100 km/h is 27.78 m/s. To convert in the other direction, multiply metres per second by 3.6. Q: What is the speed of sound and how fast is Mach 1? A: The speed of sound in dry air at 20 °C is 343 metres per second, which is 1,235 km/h or 767 mph. Mach 1 is the local speed of sound rather than a fixed value: it falls with temperature, so at typical cruising altitude, where air is around −55 °C, Mach 1 drops to roughly 295 m/s, or 1,062 km/h. Q: How fast is 60 mph in km/h? A: Sixty miles per hour is 96.56 kilometres per hour. That is why the 0-to-60 mph acceleration figure used in the United States and the 0-to-100 km/h figure used elsewhere are not directly comparable — the metric benchmark is about 3.6% faster and consistently produces a slightly longer time. Q: What is the fastest speed possible? A: The speed of light in a vacuum, exactly 299,792,458 metres per second, is the universal limit for information and matter. That value is a definition rather than a measurement: since 1983 the metre has been defined from it, which fixes the number exactly and leaves any refinement in measurement to adjust the metre instead. Sources: - The International System of Units (SI Brochure) — Bureau International des Poids et Mesures — https://www.bipm.org/en/publications/si-brochure - NIST Guide to the SI — conversion factors — US National Institute of Standards and Technology — https://www.nist.gov/pml/special-publication-811 - Standard Atmosphere and the speed of sound — NASA Glenn Research Center — https://www.grc.nasa.gov/www/k-12/airplane/atmos.html --- ### Data storage converter URL: https://truescalers.com/converters/data-storage-converter Last reviewed: 2026-08-09 A data storage converter changes a file or disk size between units, distinguishing decimal prefixes from binary ones. A megabyte is 1,000,000 bytes while a mebibyte is 1,048,576 bytes, so 1,024 MB equals 1.024 GB in decimal terms. This is why a drive sold as 1 TB reports as 931.32 GiB in an operating system. Formula: decimal: 1 kB = 1000 B binary: 1 KiB = 1024 B result = value × (factor_from ÷ factor_to) B = Byte — eight bits, the standard addressable unit of storage. kB, MB, GB, TB = Decimal SI prefixes: powers of 1,000. Used by storage manufacturers and network operators. KiB, MiB, GiB, TiB = Binary IEC prefixes: powers of 1,024. Used by operating systems and memory addressing. factor = Bytes per unit, used to route every conversion through bytes as the base. Worked example — Size: 1024, From: Megabytes (decimal, 1000²), To: Gigabytes (decimal, 1000³) → 1.024 GB Convert to bytes first: 1,024 MB × 1,000,000 = 1,024,000,000 bytes. Divide by the bytes-per-gigabyte factor: 1,024,000,000 ÷ 1,000,000,000 = 1.024 GB. The same 1,024,000,000 bytes is only 0.9537 GiB in binary terms, because a gibibyte holds 1,073,741,824 bytes. The 1,024 figure feels like exactly one gigabyte only because binary and decimal names are routinely conflated. Questions answered on this page: Q: How many MB are in a GB? A: In decimal terms, one gigabyte is 1,000 megabytes, because SI prefixes are powers of 1,000. In binary terms, one gibibyte is 1,024 mebibytes. The two are frequently confused because operating systems have long displayed binary quantities under decimal labels, showing 1,024 MiB and calling it 1 GB. Q: Why does a 1 TB hard drive show as 931 GB? A: The manufacturer sells 1 terabyte as 1,000,000,000,000 bytes using decimal prefixes. Windows divides that figure by 1,024 three times and labels the result GB, giving 931.32 — which is really 931.32 GiB. No storage is missing; the two systems are counting in different bases. The discrepancy is 9.95% at terabyte scale. Q: What is the difference between a bit and a byte? A: A bit is a single binary digit, either 0 or 1. A byte is eight bits and is the smallest individually addressable unit in most computer architectures. Storage is measured in bytes with a capital B, while network speed is measured in bits with a lowercase b — so a 100 Mbps connection transfers at most 12.5 MB per second. Q: What are KiB, MiB and GiB? A: KiB, MiB and GiB are the binary prefixes standardised in IEC 80000-13: kibibyte, mebibyte and gibibyte, equal to 1,024, 1,048,576 and 1,073,741,824 bytes respectively. The three exist to state a binary quantity unambiguously. Linux and macOS have largely adopted the correct labelling; Windows continues to display binary values under decimal names. Q: How many photos or songs fit in a gigabyte? A: One gigabyte holds roughly 250 songs at 128 kbps MP3, about 200 twelve-megapixel JPEG photographs, around 30 RAW images from a full-frame camera, or approximately eight minutes of 4K video at 100 Mbps. Compression settings dominate every one of these figures, so treat them as orders of magnitude. Q: Why is internet speed measured in megabits rather than megabytes? A: Network engineering has measured serial transmission in bits per second since the era of telegraphy, and the convention persisted. Dividing by eight converts to bytes: a 100 Mbps connection has a theoretical ceiling of 12.5 MB per second, and protocol overhead usually reduces real throughput to roughly 11 to 12 MB per second. Sources: - IEC 80000-13 — binary prefixes for information quantities — International Electrotechnical Commission — https://www.iec.ch/prefixes-binary-multiples - Prefixes for binary multiples — US National Institute of Standards and Technology — https://physics.nist.gov/cuu/Units/binary.html - The International System of Units (SI Brochure) — Bureau International des Poids et Mesures — https://www.bipm.org/en/publications/si-brochure --- ### Volume converter URL: https://truescalers.com/converters/volume-converter Last reviewed: 2026-08-09 A volume converter changes a capacity between units through litres as the base. One US gallon is exactly 3.785411784 litres and one imperial gallon is exactly 4.54609 litres, so the imperial gallon is 20.1% larger. Ten litres equals 2.6417 US gallons, and one US cup is exactly 236.5882365 millilitres. Formula: result = value × (factor_from ÷ factor_to) value = The volume being converted. factor_from = Litres per unit of the source unit — 3.785411784 for the US gallon. factor_to = Litres per unit of the target unit. result = The equivalent volume in the target unit. Worked example — Volume: 10, From: Litres, To: US gallons → 2.64172 US gallons Divide the litre value by the litres-per-US-gallon factor: 10 ÷ 3.785411784 = 2.64172 US gallons. The same ten litres is only 2.19969 imperial gallons, because the imperial gallon is larger. Expressed in US cups, 10 litres ÷ 0.2365882365 = 42.2675 cups, and in US fluid ounces it is 338.14. Questions answered on this page: Q: How many litres are in a gallon? A: A US liquid gallon is exactly 3.785411784 litres. An imperial gallon, used in the United Kingdom and some Commonwealth countries, is exactly 4.54609 litres — 20.1% larger. Fuel economy figures are therefore not comparable between the two systems: 30 miles per US gallon is 36 miles per imperial gallon. Q: How many millilitres are in a cup? A: A US legal cup used on nutrition labels is exactly 240 ml, while the US customary cup used in recipes is 236.5882365 ml. A metric cup, standard in Australia and New Zealand, is 250 ml, and a UK recipe cup is 284 ml. The 20% spread between the smallest and largest matters in baking, where ratios are precise. Q: How many tablespoons are in a cup? A: A US customary cup holds exactly 16 tablespoons, and each tablespoon holds exactly 3 teaspoons, so a cup is 48 teaspoons. An Australian tablespoon is the outlier at 20 ml rather than 15 ml — four teaspoons rather than three — which is a common source of error in recipes crossing between the two conventions. Q: What is the difference between a fluid ounce and an ounce? A: A fluid ounce measures volume; an ounce measures mass. They coincide only for water, and only approximately. A US fluid ounce is 29.5735 ml, while a UK fluid ounce is 28.4131 ml — the reverse of the gallon relationship, because the imperial gallon is divided into 160 fluid ounces rather than 128. Q: How many litres are in a cubic metre? A: Exactly 1,000. A litre is defined as one cubic decimetre, and a cubic metre contains 1,000 cubic decimetres. This makes water calculations straightforward: one cubic metre of fresh water is 1,000 litres and has a mass of almost exactly 1,000 kilograms at 4 °C, the temperature of its maximum density. Q: Should recipes be measured by volume or by weight? A: By weight, wherever precision matters. A cup of flour can vary from 120 to 150 grams depending on whether it was scooped or spooned and how much it has settled — a 25% spread that ruins bread and pastry ratios. Professional and European recipes specify grams for exactly this reason. Sources: - NIST Handbook 44 — units of volume — US National Institute of Standards and Technology — https://www.nist.gov/pml/owm/nist-handbook-44 - The International System of Units (SI Brochure) — Bureau International des Poids et Mesures — https://www.bipm.org/en/publications/si-brochure - Reference amounts and serving sizes on food labels — US Food and Drug Administration — https://www.fda.gov/food/food-labeling-nutrition --- ## PDF tools TrueScalers publishes four PDF tools: merge, split, compress, and image-to-PDF conversion. Every one runs on the pdf-lib library inside the browser, so a contract, payslip or passport scan is parsed and rebuilt on the visitor’s own device and never uploaded to a server, which is what separates these from the upload-based PDF sites. ### Merge PDF URL: https://truescalers.com/pdf-tools/merge-pdf Last reviewed: 2026-08-09 Merging PDF files combines several documents into one by copying every page from each source into a new file, in the order given. Merging a 12-page contract with a 4-page appendix produces a single 16-page document. Page dimensions, embedded fonts and image quality are all preserved exactly, because content streams are copied rather than re-encoded. Formula: output pages = Σ pages(fileᵢ) output size = Σ size(fileᵢ) − shared resources pages(fileᵢ) = The number of pages in the i-th source document. output pages = The total page count of the merged file, in the order the sources were added. shared resources = Fonts, colour profiles and images that appear in more than one source and are stored once in the output. object streams = A PDF 1.5 compression feature that packs many small objects into one compressed stream, shrinking the merged file further. Worked example — File 1: contract.pdf — 12 pages, 840 kB, File 2: appendix.pdf — 4 pages, 260 kB, File 3: signatures.pdf — 1 page, 95 kB → merged.pdf — 17 pages, about 1.1 MB The three documents contribute 12 + 4 + 1 = 17 pages, assembled in the order listed. Raw input totals 1,195 kB, but the merged file lands near 1,100 kB because the three sources share an embedded font subset that is stored once rather than three times, and because the output is written with object streams enabled. Every page keeps its original dimensions, so an A4 contract and a US Letter appendix remain their own sizes inside one file. Questions answered on this page: Q: How do you combine multiple PDF files into one? A: Add every file to the tool, confirm the order shown in the list, then press Merge. Each source document is parsed and its pages are copied page by page into a new PDF, which is assembled in the browser and offered as a download. Page order follows the file order exactly, so arranging the list correctly before merging is the only step that matters. Q: Does merging PDFs reduce quality? A: No. Merging copies each page's content stream verbatim rather than re-rendering it, so text remains selectable, vector graphics stay sharp at any zoom, and images keep the exact compression they arrived with. A merged file is never blurrier than its sources. Quality loss only happens when a PDF is compressed, which is a separate operation. Q: Is there a limit on how many PDFs can be merged? A: The tool imposes no count limit, and each file may be up to 100 MB. The practical ceiling is the memory available to the browser tab, since every document is held in memory during the merge. Merging a few dozen ordinary documents is comfortable; combining several hundred-megabyte scanned files may exhaust a low-memory device. Q: Are the PDF files uploaded to a server? A: No file is uploaded at any point. Merging runs on the pdf-lib library executing as JavaScript inside the page, so documents are read from local disk into browser memory, rebuilt there, and written back out as a download. This site has no server-side code capable of receiving a file, which is what makes the tool safe for contracts and medical records. Q: Will bookmarks, links and form fields survive a merge? A: Page content, embedded fonts and images are preserved exactly. Document-level structures behave differently: outline bookmarks and the document-wide form dictionary belong to the source file rather than to any individual page, and are not carried across. Digital signatures are always invalidated by merging, because a signature covers a specific byte range that any edit changes. Q: Can password-protected PDFs be merged? A: A PDF with an owner password restricting permissions can usually be read, but one encrypted with a user password cannot be opened without that password and will be rejected. Remove the password in a PDF reader first, then merge the unprotected copy. No password is ever transmitted, since the whole operation happens locally. Q: Why is the merged file smaller than the sum of its parts? A: Two effects shrink the output. Resources duplicated across sources — most often an embedded font subset or a shared colour profile — are written once in the merged document instead of once per file. The output is also saved using PDF object streams, which pack many small structural objects into a single compressed stream. Sources: - ISO 32000-2 — Portable Document Format — International Organization for Standardization — https://www.iso.org/standard/75839.html - PDF 1.7 specification — document structure and object streams — Adobe Systems — https://opensource.adobe.com/dc-acrobat-sdk-docs/pdfstandards/PDF32000_2008.pdf - pdf-lib — client-side PDF creation and modification — pdf-lib project — https://pdf-lib.js.org/ --- ### Split PDF URL: https://truescalers.com/pdf-tools/split-pdf Last reviewed: 2026-08-09 Splitting a PDF extracts a chosen set of pages into one or more new documents. Pages are selected by number and range, such as "1-3, 5, 8-10", which yields 7 pages. Extracted pages keep their original dimensions, fonts and image data because content streams are copied rather than re-rendered, so nothing is degraded. Formula: selection = union of ranges, clamped to 1…n and deduplicated; parts = ⌈n ÷ k⌉ n = The number of pages in the source document. ranges = Comma-separated page numbers and ranges, such as "1-3, 5, 8-10". selection = The union of every range, clamped to the document, deduplicated and sorted ascending. k = The pages per part, when splitting a document into fixed-size chunks. parts = The number of output files produced, the last of which may be shorter. Worked example — Source: report.pdf — 24 pages, Mode: Extract specific pages, Pages: 1-3, 5, 8-10 → report-pages-1-3-5-8-10.pdf — 7 pages The range "1-3" contributes pages 1, 2 and 3. The single page "5" adds one more. The range "8-10" adds pages 8, 9 and 10. The union holds 3 + 1 + 3 = 7 distinct pages, sorted ascending and clamped to the 24-page document. Those 7 pages are copied into a new PDF in ascending order regardless of the order they were typed, so entering "8-10, 1-3, 5" produces exactly the same file. Questions answered on this page: Q: How do you extract specific pages from a PDF? A: Choose "Extract specific pages", then type the page numbers and ranges you want, separated by commas — for example "1-3, 5, 8-10". Both ends of a range are included, so "1-3" gives three pages. The tool shows how many pages the selection covers before you run it, which catches a mistyped range before a file is produced. Q: Can a PDF be split into separate files for every page? A: Yes. Choose "Split every page into its own PDF" and a 24-page document produces 24 single-page files, each named after the source with a part number appended. Every output is downloaded individually, and each one keeps the page dimensions and embedded resources of the original page. Q: Does splitting a PDF reduce quality? A: No. Splitting copies each page's content stream unchanged into a new document rather than re-rendering it. Text stays selectable and searchable, vector graphics stay sharp at any zoom, and images keep their original compression. The extracted pages are byte-for-byte equivalent in content to the pages they came from. Q: Why is an extracted single page still a large file? A: A page carries its dependencies. If page 5 uses an embedded font, that font subset is copied into the new document even though only one page needs it. Scanned pages behave the same way: a single 300 DPI scanned page can be several megabytes on its own. Compressing the extracted file afterwards is the way to reduce it. Q: What happens if a page range goes past the end of the document? A: The range is clamped rather than rejected. Asking for "8-100" in a 10-page document yields pages 8, 9 and 10. A page number entirely outside the document is ignored, and overlapping ranges such as "1-5, 3-7" are merged into a single run of pages 1 to 7 rather than duplicating pages 3, 4 and 5. Q: Are files uploaded when splitting a PDF? A: No upload occurs. The document is read from local disk into browser memory, parsed by the pdf-lib library running as JavaScript in this page, and the extracted pages are written back out as a download. This site has no server-side code that could receive a file, so a confidential document stays on the device it was opened on. Sources: - ISO 32000-2 — Portable Document Format — International Organization for Standardization — https://www.iso.org/standard/75839.html - PDF 1.7 specification — page tree and content streams — Adobe Systems — https://opensource.adobe.com/dc-acrobat-sdk-docs/pdfstandards/PDF32000_2008.pdf - pdf-lib — client-side PDF creation and modification — pdf-lib project — https://pdf-lib.js.org/ --- ### Compress PDF URL: https://truescalers.com/pdf-tools/compress-pdf Last reviewed: 2026-08-09 Compressing a PDF reduces its file size by rendering each page at a lower resolution and re-encoding it as a JPEG image. A 20 MB scanned document rendered at 110 DPI with 60% JPEG quality typically drops to between 1 MB and 3 MB. The trade-off is real: selectable text, hyperlinks and form fields do not survive rasterisation. Formula: pixels per page = (width_pt ÷ 72 × DPI) × (height_pt ÷ 72 × DPI); size = pixels × bytes-per-pixel(quality) width_pt, height_pt = Page dimensions in PDF points, where 72 points equal one inch. DPI = Dots per inch the page is rendered at. 72 is screen resolution; 150 is comfortable for print. quality = The JPEG quality factor from 0 to 1, controlling how aggressively detail is discarded. pixels per page = The rasterised page area, which scales with the square of DPI. Worked example — Source: scanned-contract.pdf — 12 pages, 18.4 MB, Resolution: 110 DPI, Image quality: 60%, Greyscale: Off → scanned-contract-compressed.pdf — about 1.9 MB, a 90% reduction An A4 page is 595 × 842 points. At 110 DPI that renders to 595 ÷ 72 × 110 = 909 pixels wide and 842 ÷ 72 × 110 = 1,286 pixels tall, about 1.17 megapixels. At 60% JPEG quality a photographic page of that size encodes to roughly 150 kB, so 12 pages land near 1.8 MB plus PDF structure. The same document at 220 DPI would be four times the pixel count and roughly four times the size. Questions answered on this page: Q: How do you reduce the size of a PDF? A: The dominant cost in almost every large PDF is its images, so reducing size means reducing pixel count and image quality. This tool renders each page at a chosen DPI and re-encodes it as a JPEG. Lowering resolution from 220 to 110 DPI cuts the pixel count to a quarter, which is a far larger saving than any change to the quality slider alone. Q: Does compressing a PDF remove the selectable text? A: Yes, and that is the central trade-off. Rasterising a page turns everything on it into a single image, so text is no longer selectable, searchable or reachable by a screen reader, and hyperlinks and form fields stop working. For a scanned document nothing is lost, because the text was already an image. For a text-native PDF the loss is significant. Q: What DPI should be used for a compressed PDF? A: Use 72 to 110 DPI for documents that will only be read on a screen, where the display itself rarely exceeds about 110 effective DPI. Use 150 DPI for anything that will be printed and needs to stay legible. Above 200 DPI there is little size left to save, since the file approaches the original. Q: Why did compression barely shrink my PDF? A: A text-only PDF is already extremely efficient — a page of text may be only a few kilobytes, because it stores characters and font references rather than pixels. Rasterising such a page can even make it larger. Compression pays off on scanned documents and image-heavy reports, and is usually the wrong tool for a text-native file. Q: Is compressing a PDF lossless? A: No. This method is lossy by design: rendering at a fixed DPI discards resolution, and JPEG encoding discards detail the eye is least sensitive to. Both steps are irreversible, so keep the original. Lossless PDF optimisation — removing unused objects and recompressing streams — typically saves only 5 to 15%. Q: Does greyscale conversion actually help? A: For black-and-white scans and text documents, greyscale usually removes a further 20 to 30% because the two chroma channels are discarded entirely. Conversion uses the Rec. 709 luma weights of 0.2126 red, 0.7152 green and 0.0722 blue, which match human brightness perception; averaging the three channels equally produces a noticeably muddier result. Q: Is the PDF uploaded anywhere during compression? A: No. Pages are rendered by pdf.js and rebuilt by pdf-lib, both running as JavaScript inside this page, using the browser's own canvas and JPEG encoder. The file is read from local disk into memory and written back out as a download. This site has no server-side code capable of receiving a document. Sources: - ISO 32000-2 — Portable Document Format — International Organization for Standardization — https://www.iso.org/standard/75839.html - JPEG (ISO/IEC 10918) — image compression standard — Joint Photographic Experts Group — https://jpeg.org/jpeg/ - pdf.js — PDF rendering in the browser — Mozilla — https://mozilla.github.io/pdf.js/ --- ### Images to PDF URL: https://truescalers.com/pdf-tools/images-to-pdf Last reviewed: 2026-08-09 Converting images to PDF places each image on its own page in a new document. Page geometry is measured in PDF points, where 72 points equal one inch, so an A4 page is 595 × 842 points and US Letter is 612 × 792. JPEG images are embedded directly without re-encoding, so photo quality is preserved exactly. Formula: scale = min((W − 2m) ÷ w, (H − 2m) ÷ h); x = (W − w·scale) ÷ 2, y = (H − h·scale) ÷ 2 W, H = Page width and height in PDF points — 595 × 842 for A4, 612 × 792 for US Letter. w, h = The pixel dimensions of the image being placed. m = The margin in points applied on every side of the page. scale = The largest factor that fits the image inside the printable area without distortion. x, y = The offsets that centre the scaled image on the page. Worked example — Images: 3 photographs, each 4032 × 3024 pixels, Page size: A4 — 595 × 842 points, Margin: 24 points → images.pdf — 3 pages, one photograph per page The printable area is 595 − 48 = 547 points wide and 842 − 48 = 794 points tall. The scale factor is the smaller of 547 ÷ 4032 = 0.1357 and 794 ÷ 3024 = 0.2626, so 0.1357 governs. The drawn image is 4032 × 0.1357 = 547 points wide and 3024 × 0.1357 = 410 points tall. It is centred with an x offset of (595 − 547) ÷ 2 = 24 points and a y offset of (842 − 410) ÷ 2 = 216 points. Questions answered on this page: Q: How do you convert JPG images to a PDF? A: Add the images, choose a page size, and press Create PDF. Each image is placed on its own page, scaled to fit inside the margins while preserving its aspect ratio, and centred. JPEG files are embedded byte-for-byte without re-encoding, so a photograph inside the resulting PDF is pixel-identical to the file that went in. Q: Does converting images to PDF reduce their quality? A: JPEG images are embedded directly with no re-encoding, so no quality is lost at all. PNG images are also embedded losslessly. Other formats such as WebP, GIF and BMP have no native PDF representation and are re-encoded to JPEG at 92% quality first, which is visually lossless for photographs but is a genuine re-encode. Q: What is a PDF point and how does it relate to inches? A: A PDF point is exactly 1/72 of an inch, inherited from typographic measurement. That makes A4 595 × 842 points, US Letter 612 × 792 points, and a one-inch margin exactly 72 points. Because points are physical rather than pixel units, a PDF prints at the same size regardless of the screen it was made on. Q: Should page size be A4, Letter, or fit-to-image? A: Choose A4 or US Letter when the document will be printed or emailed, since a uniform page size is what recipients and printers expect — A4 outside North America, Letter within it. Choose fit-to-image for screen-only use such as an image archive or comic, where matching each page to its image avoids both margins and scaling. Q: Why is the resulting PDF larger than the images it contains? A: A PDF adds structural overhead: a page tree, a cross-reference table, resource dictionaries and metadata. For a handful of large photographs this overhead is a fraction of a percent. It is only noticeable when embedding many very small images, where the per-page structure can rival the image data itself. Q: Are the images uploaded to make the PDF? A: No. Images are read from local disk into browser memory and embedded into a document assembled by the pdf-lib library running as JavaScript in this page. The finished PDF is handed straight to the browser as a download. This site has no server-side code that could receive an image, so personal photographs never leave the device. Sources: - ISO 32000-2 — Portable Document Format — International Organization for Standardization — https://www.iso.org/standard/75839.html - ISO 216 — A-series paper sizes — International Organization for Standardization — https://www.iso.org/standard/36631.html - pdf-lib — embedding images in PDF documents — pdf-lib project — https://pdf-lib.js.org/ --- ## Image tools TrueScalers publishes three image tools: a resizer, a compressor and a format converter supporting JPEG, PNG and WebP. All three decode and re-encode images using the browser’s own canvas and codecs, so a photograph is processed on the visitor’s device. Batches are supported, and no image is uploaded at any point. ### Image resizer URL: https://truescalers.com/image-tools/image-resizer Last reviewed: 2026-08-09 Resizing an image changes its pixel dimensions. Fitting inside a bounding box uses the smaller of the two ratios, so a 4000 × 3000 photograph constrained to 1920 × 1080 becomes 1440 × 1080, not 1920 × 1080 — using the larger ratio would distort it. This tool resizes in batches inside the browser. Formula: scale = min(maxW ÷ w, maxH ÷ h); w′ = round(w × scale), h′ = round(h × scale) w, h = The original pixel width and height of the image. maxW, maxH = The bounding box the image must fit inside. scale = The smaller of the two ratios, which guarantees both dimensions fit. w′, h′ = The resulting dimensions, rounded to whole pixels. Worked example — Source: photo.jpg — 4000 × 3000 pixels, 5.2 MB, Max width: 1920 px, Max height: 1080 px → 1440 × 1080 pixels, about 480 kB The width ratio is 1920 ÷ 4000 = 0.48 and the height ratio is 1080 ÷ 3000 = 0.36. The smaller value, 0.36, is used so both dimensions fit inside the box. The result is 4000 × 0.36 = 1440 wide and 3000 × 0.36 = 1080 tall. Pixel count falls from 12.0 megapixels to 1.56 megapixels, a reduction of 87%, and file size falls by roughly the same proportion because JPEG size scales with pixel count. Questions answered on this page: Q: How do you resize an image without distorting it? A: Scale both dimensions by the same factor. To fit inside a bounding box, take the smaller of width ratio and height ratio: for a 4000 × 3000 image going into 1920 × 1080, that is 1080 ÷ 3000 = 0.36, producing 1440 × 1080. Applying the larger ratio would fill the box exactly but stretch the picture, which is the usual cause of squashed-looking photos. Q: Does resizing an image reduce its quality? A: Downscaling discards pixels and is irreversible, but done properly it looks clean because each output pixel averages many input pixels. Upscaling is the damaging direction: enlarging invents detail that was never captured, so it always looks softer than the original. This tool refuses to enlarge unless percentage mode is used with a value above 100. Q: What image size should be used on a website? A: Match the largest size the image will ever be displayed at, then account for high-density screens. A full-width hero on a 1440-pixel layout wants roughly 2880 pixels for a 2× display. A content image spanning 680 pixels wants about 1360. Serving a 4000-pixel photograph into a 680-pixel slot wastes roughly 97% of the bytes downloaded. Q: What is the difference between resizing and cropping? A: Resizing scales the whole image to different pixel dimensions and keeps every part of the picture. Cropping removes area from the edges and keeps the remaining pixels at their original scale. Resizing changes how large the image is; cropping changes what the image contains. Changing aspect ratio without distortion requires cropping, not resizing. Q: Does resizing keep image transparency? A: Transparency survives when the output format supports it. PNG and WebP both carry an alpha channel, so a transparent background stays transparent. JPEG has no alpha channel at all, so converting a transparent PNG to JPEG fills the transparent areas with white, which is why a logo saved as JPEG gains a visible box. Q: Are images uploaded when they are resized? A: No. Each file is decoded with the browser's own image decoder, redrawn onto a canvas at the target size, and re-encoded using the browser's built-in codecs. Everything happens in the page. This site has no server-side code capable of receiving an image, so private photographs are never transmitted. Sources: - Canvas 2D — drawImage and image smoothing — WHATWG HTML Standard — https://html.spec.whatwg.org/multipage/canvas.html - Serve images in modern formats and correct sizes — Google web.dev — https://web.dev/articles/serve-responsive-images - createImageBitmap and EXIF orientation handling — Mozilla Developer Network — https://developer.mozilla.org/en-US/docs/Web/API/createImageBitmap --- ### Image compressor URL: https://truescalers.com/image-tools/image-compressor Last reviewed: 2026-08-09 Compressing an image reduces its file size by discarding detail the eye is least sensitive to. JPEG quality 75 typically removes 60 to 80% of a photograph's bytes with no visible difference at normal viewing distance. This tool can also hit an exact target size by binary-searching the quality factor across seven encodes. Formula: find the largest quality q between 0.30 and 0.95 for which size(q) fits within target q = The JPEG or WebP quality factor, from 0.30 at the low end to 0.95 at the high end. size(q) = The encoded file size in bytes at quality q, which increases monotonically with q. target = The requested maximum file size in bytes. binary search = Halving the quality interval seven times, which locates q to within 0.5% using 7 encodes instead of up to 65. Worked example — Source: photo.jpg — 4032 × 3024 pixels, 5.2 MB, Quality: 75%, Target size: not set → about 890 kB — an 83% reduction The image keeps its 4032 × 3024 dimensions, so all 12.2 megapixels remain. Re-encoding at quality 75 discards high-frequency detail within each 8 × 8 block that the eye barely registers, taking the file from 5.2 MB to roughly 890 kB. That is a saving of 4.3 MB, or 83%, with no change in resolution. Setting a 500 kB target instead would make the encoder binary-search quality and settle near 0.55. Questions answered on this page: Q: What is the best quality setting for JPEG compression? A: Quality 75 to 80 is the standard recommendation for photographs and is where most of the size saving happens. Below 60, blocking artefacts start appearing in smooth gradients such as skies. Above 90 the file grows sharply for detail almost nobody can see — moving from 80 to 95 can double the file size for a barely perceptible gain. Q: How do you compress an image to an exact file size? A: Enter a target in kilobytes and the tool encodes repeatedly, halving the quality interval each time, until it finds the highest quality that still fits. Seven encodes locate the quality factor to within about 0.5%. This is how you meet a hard limit such as a 200 kB upload cap or a 2 MB email attachment ceiling. Q: Is image compression lossy or lossless? A: JPEG and WebP quality settings are lossy: discarded detail is gone permanently, and re-compressing an already-compressed image degrades it further. PNG is lossless, so its size is reduced only by simplifying the palette rather than by any quality factor. Always keep the original file, because compression cannot be undone. Q: Why did compressing my PNG barely help? A: PNG uses lossless DEFLATE compression, which has no quality dial to turn down. A photograph stored as PNG is enormous because lossless coding cannot exploit the eye's insensitivity to fine detail. Converting a photographic PNG to JPEG or WebP typically cuts it by 80 to 95%; keep PNG only for logos, screenshots and images needing transparency. Q: Does compression change image dimensions? A: No. Compression keeps every pixel and reduces how many bytes each one costs. Resizing is the separate operation that changes pixel dimensions. Combining both gives the largest savings: a 4000-pixel photograph resized to 1600 pixels and then compressed at quality 75 is routinely 95% smaller than the original. Q: How much can compression improve page load speed? A: Images are usually the largest asset class on a web page, so the effect is direct. Cutting 5 MB of photographs to 900 kB removes about 4 MB from the download, roughly 4 seconds on a 8 Mbps mobile connection. Because images frequently form the Largest Contentful Paint element, that saving lands squarely on a Core Web Vital. Q: Are images uploaded to compress them? A: No. Each file is decoded and re-encoded by the browser's own image codecs inside this page. Nothing is transmitted, and this site has no server-side code that could receive a file. That makes the tool safe for photographs of documents, identification and anything else you would not paste into a website. Sources: - JPEG (ISO/IEC 10918) — image compression standard — Joint Photographic Experts Group — https://jpeg.org/jpeg/ - WebP compression techniques and comparison — Google — https://developers.google.com/speed/webp/docs/compression - Optimize images to improve Largest Contentful Paint — Google web.dev — https://web.dev/articles/optimize-lcp --- ### Image converter URL: https://truescalers.com/image-tools/image-converter Last reviewed: 2026-08-09 Converting an image format changes how its pixels are encoded. WebP produces files roughly 25 to 35% smaller than JPEG at equivalent quality and, unlike JPEG, supports transparency. Converting a transparent PNG to JPEG fills transparent areas with white, because the JPEG format has no alpha channel to store them in. Formula: decode(source) → pixel buffer → encode(target, quality) decode = Reading the source file into a raw pixel buffer using the browser image decoder. pixel buffer = The uncompressed RGBA data, four bytes per pixel, that both formats are derived from. encode = Writing the buffer back out in the target format at the chosen quality. quality = The lossy quality factor, applied for JPEG and WebP and ignored for PNG, which is lossless. Worked example — Source: photo.jpg — 4032 × 3024 pixels, 2.4 MB, Convert to: WebP, Quality: 85% → photo-webp.webp — about 1.6 MB, 33% smaller The JPEG is decoded to a 4032 × 3024 pixel buffer, which is 12.2 megapixels or roughly 48.8 MB uncompressed at 4 bytes per pixel. That buffer is re-encoded as WebP at quality 85, landing near 1.6 MB against the original 2.4 MB — a saving of 33% at visually equivalent quality. Converting the same buffer to PNG instead would produce a file of roughly 20 MB, because lossless coding cannot discard photographic detail. Questions answered on this page: Q: Which image format should be used on a website? A: WebP is the default choice in 2026: it is 25 to 35% smaller than JPEG at equivalent quality, supports transparency and animation, and works in every browser released since 2020. Keep JPEG for maximum compatibility with older software, and PNG only for screenshots, logos and anything needing a genuinely lossless copy. Q: What is the difference between JPEG and PNG? A: JPEG is lossy and designed for photographs, discarding fine detail the eye barely registers to achieve large size reductions. PNG is lossless and designed for graphics with flat colour and sharp edges, and it supports transparency. A photograph stored as PNG is typically five to ten times larger than the same image as JPEG. Q: Why did my PNG get a white background when converted to JPEG? A: JPEG has no alpha channel, so transparency cannot be represented in the format at all. Transparent pixels must be composited against something, and white is the conventional choice. To keep a transparent background, convert to WebP or PNG instead — both carry an alpha channel. Q: Does converting JPEG to PNG improve quality? A: No. Detail discarded by the original JPEG encoding is gone permanently, and PNG merely stores those already-degraded pixels without further loss. The result looks identical to the JPEG while occupying far more space. Converting to PNG is worthwhile only when a lossless working copy is needed for further editing. Q: Is WebP supported everywhere? A: Yes, in practice. WebP is supported by Chrome, Edge, Firefox, Safari 14 and above, and every current mobile browser, which covers well over 95% of traffic. The remaining gaps are old desktop software and some email clients, so JPEG remains the safer choice for email attachments and files handed to unknown recipients. Q: What about AVIF and HEIC? A: AVIF compresses better than WebP, often by a further 20%, but encoding is considerably slower and browser support arrived later. HEIC is the default on iPhones and is largely unsupported outside Apple platforms, which is why iPhone photos frequently need converting before sharing. This tool reads HEIC only where the browser itself can decode it. Q: Are files uploaded during conversion? A: No. Each image is decoded and re-encoded using the browser's own built-in codecs, entirely inside this page. Nothing is transmitted, and this site has no server-side code that could receive a file. Converting a photograph of a passport or a private document is therefore no different from doing it in a desktop application. Sources: - WebP compression techniques and comparison — Google — https://developers.google.com/speed/webp/docs/compression - PNG (Portable Network Graphics) specification — World Wide Web Consortium — https://www.w3.org/TR/png-3/ - JPEG (ISO/IEC 10918) — image compression standard — Joint Photographic Experts Group — https://jpeg.org/jpeg/ --- ## Generators TrueScalers publishes three generators: a password generator, a random number generator and a version 4 UUID generator. All three draw from the Web Crypto cryptographically secure pseudorandom number generator inside the browser, so generated values are never transmitted to a server, logged, or recoverable after the page is closed. ### QR code generator URL: https://truescalers.com/generators/qr-code-generator Last reviewed: 2026-08-09 A QR code stores data in a square grid of modules read optically in two dimensions. Error correction level M recovers the code when up to 15% of it is damaged or covered, and level H raises that to 30%. A version 4 code holds 33 × 33 modules and encodes up to 78 alphanumeric characters at level M. Formula: modules = 4 × version + 17, version from 1 to 40 version = The QR symbol version from 1 to 40, chosen automatically from the data length and error-correction level. modules = The grid width in modules — 21 × 21 at version 1, rising to 177 × 177 at version 40. error correction = Reed-Solomon redundancy at level L, M, Q or H, recovering 7%, 15%, 25% or 30% of the symbol respectively. quiet zone = The blank margin around the symbol, required by the standard to be at least 4 modules wide. Worked example — Content: https://truescalers.com, Error correction: M — recovers 15% damage, Size: 512 px, Quiet zone: 2 modules → Version 2 — a 25 × 25 module grid, exported at 512 × 512 pixels The URL is 23 characters, which fits inside version 2 at error-correction level M. Version 2 gives 4 × 2 + 17 = 25 modules per side. Exported at 512 pixels, each module is 512 ÷ 25 ≈ 20.5 pixels square, comfortably above the 4-pixel minimum any camera needs to resolve. Raising error correction to level H on the same content would push the symbol to version 3, a 29 × 29 grid, because redundancy takes space the payload previously used. Questions answered on this page: Q: How does a QR code work? A: A QR code encodes data as a grid of black and white modules read in two dimensions. Three large squares in the corners let a scanner find and orient the symbol regardless of rotation, and Reed-Solomon error correction lets it reconstruct the data even when part of the code is damaged, dirty or obscured. Q: What error correction level should be used? A: Level M, recovering 15%, is the sensible default for a code displayed on a screen. Level Q at 25% or level H at 30% suit printed material, outdoor signage and anything likely to be scuffed or partly covered. Placing a logo over the centre of a code requires level H, since the logo destroys modules the scanner must reconstruct. Q: Do these QR codes expire or track scans? A: Neither. The code generated here is static: the destination is encoded directly into the pattern, so it works forever and no server sits between the scanner and the destination. Many free generators produce dynamic codes that point at their own redirect domain, which lets them count scans and disable the code later, often behind a subscription. Q: How much data fits in a QR code? A: The maximum at version 40 with error correction level L is 7,089 numeric digits, 4,296 alphanumeric characters, or 2,953 bytes. Practical limits are far lower: past roughly 300 characters the modules become too small to scan reliably from a phone at arm's length unless the code is printed large. Q: What size should a printed QR code be? A: The usual rule is that the code should be at least one tenth of the scanning distance. A code read from 30 centimetres needs to be about 3 centimetres square; one read from 3 metres needs about 30 centimetres. Add the mandatory quiet zone of at least four modules, and never print smaller than 2 centimetres. Q: Can QR code colours be changed? A: Yes, provided contrast stays high and polarity is preserved — the foreground must be darker than the background, because scanners expect dark modules on a light field. Inverting that breaks many readers. Keep a contrast ratio of at least 4:1, avoid gradients across the symbol, and always test the finished code on a real phone. Q: How does a Wi-Fi QR code work? A: A Wi-Fi code encodes a specific string, "WIFI:T:WPA;S:network;P:password;;", which phones recognise and turn into a join-network prompt. The password is stored in plain text inside the pattern, so anyone who scans or photographs the code obtains it — that is fine for a guest network printed on a café card, and unwise for a primary network. Sources: - ISO/IEC 18004 — QR Code bar code symbology specification — International Organization for Standardization — https://www.iso.org/standard/83389.html - QR Code capacity, versions and error correction levels — Denso Wave — https://www.qrcode.com/en/about/version.html - Barcode Contents — payload formats for scanners — ZXing project — https://github.com/zxing/zxing/wiki/Barcode-Contents --- ### Password generator URL: https://truescalers.com/generators/password-generator Last reviewed: 2026-08-09 A password generator produces a random string from a chosen character pool. Password strength is measured as entropy in bits, calculated as E = L × log₂(R), where L is the length and R is the pool size. A 20-character password drawn from 94 printable ASCII symbols carries 131 bits of entropy, which is beyond the reach of any brute-force attack. Formula: E = L × log₂(R) E = Entropy in bits — the base-2 logarithm of the number of equally likely passwords. L = Password length in characters. R = The size of the character pool each position is drawn from. log₂ = The base-2 logarithm. Worked example — Length: 20 characters, Character sets: Lowercase, uppercase, digits, symbols, Exclude look-alikes: No → 128.5 bits of entropy — very strong The enabled sets contribute 26 lowercase, 26 uppercase, 10 digits and 24 symbols, giving a pool of 86 characters. Entropy is 20 × log₂(86) = 20 × 6.4263 = 128.5 bits. That corresponds to roughly 3.4 × 10³⁸ possible passwords. At ten billion guesses per second, exhausting half that keyspace would take on the order of 5 × 10²⁰ years — many orders of magnitude beyond the age of the universe. Questions answered on this page: Q: How long should a password be? A: Length contributes more to strength than complexity does. Sixteen characters from a mixed pool gives roughly 103 bits of entropy, comfortably beyond offline brute-force reach. NIST Special Publication 800-63B recommends a minimum of 8 characters and support for at least 64, and explicitly advises against forced composition rules and periodic mandatory rotation. Q: What makes a password strong? A: Strength is unpredictability, measured as entropy in bits. A password is strong when it is generated uniformly at random from a large pool and is long enough that the keyspace is infeasible to search. Substitutions such as replacing "a" with "@" add almost nothing, because password-cracking tools apply those transformations automatically. Q: Is this password generator safe to use? A: Generation happens entirely inside your browser using the Web Crypto API's cryptographically secure pseudorandom number generator. No password is sent over the network, written to storage, or logged — this site has no server-side code that could receive one. Closing the tab destroys the value permanently. Q: Should I use a passphrase instead? A: A passphrase of random words is an excellent choice where a password must be memorised. Six words drawn randomly from the 7,776-word Diceware list carry 77.5 bits of entropy — strong, and far easier to remember than a comparable random string. For passwords stored in a manager, memorability is irrelevant and a longer random string is preferable. Q: How often should passwords be changed? A: Only when there is evidence of compromise. NIST SP 800-63B reversed the long-standing rotation advice because forced periodic changes push users toward predictable variations such as appending an incrementing digit. A unique, high-entropy password per account, held in a manager, is materially stronger than a rotated weak one. Q: What is entropy in bits and what number is enough? A: Entropy in bits is the base-2 logarithm of the number of equally likely values a password could have taken. Each additional bit doubles the search space. Below 28 bits is trivially broken, 60 bits resists most online attacks, 80 bits is robust, and anything at or above 128 bits is beyond brute force with any foreseeable technology. Q: Why does excluding look-alike characters reduce strength? A: Removing 0, O, o, 1, l and I shrinks the character pool from 86 to 80, lowering entropy per character from 6.43 to 6.32 bits. Over a 20-character password that costs about 2 bits in total — a negligible trade for eliminating transcription errors when the password must be read aloud or copied by hand. Sources: - NIST SP 800-63B — Digital Identity Guidelines, Authentication — US National Institute of Standards and Technology — https://pages.nist.gov/800-63-3/sp800-63b.html - Web Crypto API — getRandomValues specification — World Wide Web Consortium — https://www.w3.org/TR/WebCryptoAPI/ - Password guidance — simplifying your approach — UK National Cyber Security Centre — https://www.ncsc.gov.uk/collection/passwords --- ### Random number generator URL: https://truescalers.com/generators/random-number-generator Last reviewed: 2026-08-09 A random number generator draws integers uniformly from a range using X = min + ⌊U × (max − min + 1)⌋, where U is a uniform random value from the browser cryptographic random source. Drawing from 1 to 100 gives every value an equal 1% probability. Selecting six unique numbers from 1 to 49 samples without replacement, so no value repeats. Formula: X = min + ⌊U × (max − min + 1)⌋, U uniform on [0, 1) X = The generated integer. min = The lowest value in the range, inclusive. max = The highest value in the range, inclusive. U = A uniform random value in [0, 1) from the Web Crypto CSPRNG. ⌊ ⌋ = The floor function, discarding the fractional part. Worked example — Minimum: 1, Maximum: 100, How many: 1, No repeats: Off → One integer between 1 and 100 The range spans max − min + 1 = 100 values, so every integer from 1 to 100 has probability 1 ÷ 100 = 1.00%. The generator requests a 32-bit unsigned value from the Web Crypto API, divides it by 2³² to obtain a uniform value U in [0, 1), multiplies by 100, takes the floor, and adds the minimum. Requesting six unique values from 1 to 49 instead gives each of the 13,983,816 possible combinations an equal chance. Questions answered on this page: Q: Are these numbers genuinely random? A: Every value is drawn from the Web Crypto API's cryptographically secure pseudorandom number generator, seeded by operating-system entropy from hardware sources. Output is computationally indistinguishable from true randomness and is suitable for prize draws, sampling and key material. It is not a hardware quantum source, but no statistical test can distinguish the two. Q: What is the difference between a CSPRNG and Math.random? A: Math.random uses a fast non-cryptographic algorithm whose internal state can be recovered from a modest number of observed outputs, making all future values predictable. A cryptographically secure generator is built so that recovering state or predicting future output is computationally infeasible. Anything with a prize, a stake, or a secret attached requires the secure generator. Q: How do you pick a random winner fairly? A: Assign each entry a sequential number from 1 to N, then draw one integer in that range. For multiple winners, enable no-repeats so the same entry cannot be drawn twice. Recording the entry list before drawing, and drawing once rather than repeatedly, is what makes the process auditable and defensible. Q: What does sampling without replacement mean? A: Sampling without replacement removes each drawn value from the pool, so no value can appear twice — the model for a lottery draw or a raffle. Sampling with replacement returns each value to the pool, so repeats are possible, which is the model for rolling a die repeatedly. The two produce measurably different probability distributions. Q: Can this generator be used for a lottery or a giveaway? A: Informal draws, classroom selection and giveaway winner picking are all appropriate uses. Regulated gambling and formal prize promotions are subject to jurisdiction-specific rules that often require certified randomness sources and independent audit. Check the applicable regulator's requirements before relying on any browser tool for a legally binding draw. Q: Why do random numbers sometimes repeat or cluster? A: Clustering is what genuine randomness looks like. Sequences that alternate evenly are the ones that are not random. Drawing ten numbers from 1 to 100 gives roughly a 37% chance of at least one duplicate — the birthday problem — and streaks of similar values are expected. Enable no-repeats when duplicates are unwanted. Sources: - Web Crypto API — getRandomValues specification — World Wide Web Consortium — https://www.w3.org/TR/WebCryptoAPI/ - NIST SP 800-90A — random bit generation — US National Institute of Standards and Technology — https://csrc.nist.gov/pubs/sp/800/90/a/r1/final - A statistical test suite for random number generators — US National Institute of Standards and Technology — https://csrc.nist.gov/pubs/sp/800/22/r1/upd1/final --- ### UUID generator URL: https://truescalers.com/generators/uuid-generator Last reviewed: 2026-08-09 A version 4 UUID is a 128-bit identifier in which 122 bits are random, with 4 bits fixed as the version and 2 bits as the variant. That yields 2¹²², or approximately 5.32 × 10³⁶, distinct values. UUIDs are written as 32 hexadecimal digits in the 8-4-4-4-12 pattern, such as 3f2504e0-4f89-41d3-9a0c-0305e82c3301. Formula: xxxxxxxx-xxxx-4xxx-Nxxx-xxxxxxxxxxxx where N is one of 8, 9, a or b 4 = The version nibble, fixed at 4 to identify a randomly generated UUID. 122 = The number of genuinely random bits, after the 6 fixed version and variant bits. x = A random hexadecimal digit, contributing 4 bits each. N = The variant nibble. Its two most significant bits are set to 10, restricting it to 8, 9, a or b. Worked example — How many: 5, Uppercase: No, Braces: No, Hyphens: Yes → Five version 4 UUIDs, e.g. 3f2504e0-4f89-41d3-9a0c-0305e82c3301 Sixteen random bytes are requested from the Web Crypto CSPRNG. Byte 6 has its high nibble replaced with 4 to mark the version, and byte 8 has its two most significant bits set to 10 to mark the variant. The remaining 122 bits stay random. The bytes are then rendered as 32 lowercase hexadecimal digits and grouped 8-4-4-4-12. Generating one billion per second for a century would leave the collision probability below one in a billion. Questions answered on this page: Q: What is a UUID? A: A universally unique identifier is a 128-bit value used to label something without a central authority issuing the labels. Any system can generate one independently and rely on it not colliding with an identifier generated elsewhere. UUIDs are standardised in RFC 9562 and are written as 32 hexadecimal digits grouped as 8-4-4-4-12. Q: What is the difference between UUID versions? A: Version 1 encodes a timestamp and a MAC address, which leaks host information. Version 3 and version 5 hash a name within a namespace, producing deterministic identifiers. Version 4 is purely random. Version 7, added in RFC 9562, prefixes a Unix millisecond timestamp to random bits, making identifiers sort chronologically while remaining unpredictable. Q: Can two UUIDs ever be the same? A: A collision is possible but negligible. With 2¹²² random values, generating one billion UUIDs per second for 100 years leaves the probability of a single collision below one in a billion. Reaching a 50% collision chance would require roughly 2.7 × 10¹⁸ identifiers. In practice, collisions arise from a broken random source, never from exhausting the space. Q: Should a UUID be used as a database primary key? A: The database engine decides. Version 4 UUIDs are random, so inserting them into a clustered B-tree index causes page splits and index fragmentation, hurting write throughput at scale. Version 7 UUIDs are time-ordered and avoid that problem. PostgreSQL handles random UUIDs better than clustered-index engines such as MySQL with InnoDB. Q: Is a UUID secure enough to use as a secret token? A: A version 4 UUID carries 122 bits of entropy from a cryptographic source, which is sufficient for an unguessable identifier such as a password-reset token. Versions 1, 3 and 5 are not, because they are derived from timestamps, MAC addresses or hashed names and are therefore predictable or reconstructible. Q: What is the difference between a UUID and a GUID? A: The two terms describe the same thing. GUID, for globally unique identifier, is Microsoft's name for the format and appears throughout Windows and .NET APIs. Microsoft conventionally renders them in uppercase and wrapped in braces, but the underlying 128-bit value and the RFC 9562 layout are identical. Sources: - RFC 9562 — Universally Unique IDentifiers (UUIDs) — IETF — https://www.rfc-editor.org/rfc/rfc9562.html - Web Crypto API — getRandomValues specification — World Wide Web Consortium — https://www.w3.org/TR/WebCryptoAPI/ - NIST SP 800-90A — random bit generation — US National Institute of Standards and Technology — https://csrc.nist.gov/pubs/sp/800/90/a/r1/final --- ## Developer tools TrueScalers publishes five developer tools: a JSON formatter and validator, a Base64 encoder, a URL encoder, a SHA hash generator and a regular-expression tester. Each runs entirely in the browser using native JavaScript and the Web Crypto API, so API keys, tokens and production payloads pasted into them are never transmitted or logged. ### JSON formatter URL: https://truescalers.com/developer-tools/json-formatter Last reviewed: 2026-08-09 A JSON formatter parses a JSON document and re-prints it with consistent indentation, reporting the line and column of any syntax error. Minifying removes all insignificant whitespace, which typically cuts a formatted payload by 15 to 30%. This formatter runs in the browser, so production payloads containing tokens are never transmitted. Formula: JSON.parse(text) → value → JSON.stringify(value, null, indent) JSON.parse = The native parser, which either returns a value or throws with a byte offset for the first syntax error. value = The resulting JavaScript value — an object, array, string, number, boolean or null. indent = Spaces per nesting level when pretty-printing. Passing no indent produces minified output. depth = The deepest level of nesting in the document, reported alongside key, object and array counts. Worked example — Input: {"name":"TrueScalers","tools":27,"meta":{"reviewed":"2026-08-09"}}, Indent: 2 spaces, Minify: off → Valid JSON — 3 keys, 2 objects, 2 levels deep The parser reads the 66-character input and produces an object with 2 top-level keys plus 1 nested key, giving 3 keys across 2 objects and no arrays. Re-printing with 2-space indentation expands it to 6 lines and about 110 bytes, because each nesting level adds whitespace. Minifying the same value returns it to 66 bytes, a 40% reduction — which is exactly why APIs send minified JSON and developers read formatted JSON. Questions answered on this page: Q: How do you find a syntax error in JSON? A: The parser reports the byte offset where it stopped, which is converted here into a line and column number. The most common causes are a trailing comma after the last element, a single quote used instead of a double quote, an unquoted key, and an unescaped newline inside a string. The reported position is where parsing failed, which is sometimes just after the real mistake. Q: What is the difference between formatting and minifying JSON? A: Formatting adds newlines and indentation so a human can read the structure. Minifying removes every byte of insignificant whitespace so a machine can transfer it efficiently, typically cutting 15 to 30% from a formatted document. Both represent exactly the same value, so an API can send minified JSON and a developer can read the formatted form. Q: Are comments allowed in JSON? A: No. RFC 8259 defines no comment syntax, and a standard parser rejects any document containing one. Supersets such as JSON5 and JSONC add comments and are used in configuration files including tsconfig.json, but they are not JSON and will not parse here. Strip comments before validating against the standard. Q: Why does sorting JSON keys matter? A: Object key order is not semantically meaningful in JSON, but a textual diff treats reordered keys as changes. Sorting both documents alphabetically before comparing makes a diff show only genuine differences. Sorting also produces a canonical form, which is useful when hashing a payload to detect whether its content has actually changed. Q: Is it safe to paste API responses into this tool? A: Yes. Parsing and formatting happen entirely in this page using the browser's native JSON implementation, and this site has no server-side code capable of receiving text. Nothing is transmitted, logged or stored, so a payload containing an access token or customer data is no more exposed than in a local text editor. Q: Why did my large numbers change after formatting? A: JSON numbers are parsed into IEEE 754 double-precision floats, which represent integers exactly only up to 2⁵³ − 1, or 9,007,199,254,740,991. A 19-digit database identifier exceeds that and is silently rounded. Systems that must preserve such values transmit them as strings, which is why many APIs quote their ID fields. Sources: - RFC 8259 — The JavaScript Object Notation (JSON) Data Interchange Format — IETF — https://www.rfc-editor.org/rfc/rfc8259.html - ECMA-404 — The JSON Data Interchange Syntax — Ecma International — https://ecma-international.org/publications-and-standards/standards/ecma-404/ - IEEE 754 double-precision and safe integers — Mozilla Developer Network — https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/MAX_SAFE_INTEGER --- ### Base64 encoder URL: https://truescalers.com/developer-tools/base64-encoder Last reviewed: 2026-08-09 Base64 encodes binary data as 64 printable ASCII characters, representing every 3 bytes as 4 characters. Encoded output is therefore about 33% larger than the input. "Hello, World!" is 13 bytes and encodes to the 20-character string SGVsbG8sIFdvcmxkIQ==, where the trailing equals signs pad the final group. Formula: encoded length = 4 × ⌈n ÷ 3⌉, overhead is 33.3% n = The number of input bytes — not characters, since one UTF-8 character can be up to 4 bytes. encoded length = The output length in characters, always a multiple of 4 when padded. = = Padding appended so the output length is a multiple of 4. One byte remaining adds "==", two bytes adds "=". alphabet = A–Z, a–z, 0–9 and + / in the standard variant; - and _ replace + and / in the URL-safe variant. Worked example — Input: Hello, World!, Direction: Encode text to Base64, URL-safe: off → SGVsbG8sIFdvcmxkIQ== The input is 13 bytes of ASCII. Base64 processes 3 bytes at a time, so 13 bytes form 4 complete groups of 3 with 1 byte left over: ⌈13 ÷ 3⌉ = 5 groups. Each group becomes 4 characters, giving 20 characters of output. The final group holds only 1 byte, so it produces 2 meaningful characters plus "==" of padding. Output is 20 characters against 13 input bytes, the expected 33% overhead. Questions answered on this page: Q: What is Base64 used for? A: Base64 moves binary data through channels that only accept text. Common uses are embedding small images directly in CSS or HTML as data URIs, attaching files to email under MIME, carrying credentials in an HTTP Basic authorization header, and placing binary blobs inside JSON, which has no native binary type. Q: Is Base64 encryption? A: No, and treating it as such is a genuine security mistake. Base64 is a reversible encoding with no key: anyone can decode it in one step. Credentials in an HTTP Basic header are Base64-encoded, not protected, which is exactly why Basic authentication is only safe over HTTPS where the transport provides the encryption. Q: Why does Base64 make data larger? A: Base64 represents 3 bytes of input using 4 output characters, because each output character carries only 6 bits of information rather than 8. That is a fixed 33.3% expansion, plus up to 2 characters of padding. Embedding a 100 kB image as a data URI therefore costs about 133 kB in the document. Q: What is URL-safe Base64? A: The standard alphabet includes + and /, which have reserved meanings in URLs, and = padding, which conflicts with query-string syntax. The URL-safe variant defined in RFC 4648 section 5 substitutes - for + and _ for / and omits the padding. JSON Web Tokens use this variant for every one of their three segments. Q: Why does encoding fail on emoji or accented characters? A: The browser's built-in btoa function operates on Latin-1 and throws on any character above U+00FF, so "café" and every emoji fail outright. This tool encodes the text to UTF-8 bytes first and Base64-encodes those bytes, which handles the full Unicode range correctly and round-trips exactly. Q: How do you know if a string is valid Base64? A: Valid Base64 contains only characters from its alphabet, and its length is a multiple of 4 once padding is included. This tool restores missing padding automatically, since URL-safe output legitimately omits it, and reports an error if any character falls outside the alphabet or the length cannot be reconciled. Q: Is pasted data sent anywhere? A: No. Encoding and decoding happen entirely in this page using JavaScript running in your browser. Nothing is transmitted, logged or stored, and this site has no server-side code capable of receiving text. Decoding a JWT that contains customer data or an internal token is therefore safe here. Sources: - RFC 4648 — The Base16, Base32, and Base64 Data Encodings — IETF — https://www.rfc-editor.org/rfc/rfc4648.html - RFC 2045 — MIME Part One, including Base64 content transfer encoding — IETF — https://www.rfc-editor.org/rfc/rfc2045.html - RFC 7519 — JSON Web Token — IETF — https://www.rfc-editor.org/rfc/rfc7519.html --- ### URL encoder URL: https://truescalers.com/developer-tools/url-encoder Last reviewed: 2026-08-09 URL encoding replaces unsafe characters with a percent sign followed by two hexadecimal digits of their UTF-8 bytes. A space becomes %20 and an ampersand becomes %26. Component mode escapes the reserved delimiters & = ? / # so a value is safe inside one query parameter; whole-URL mode leaves them intact so the URL structure survives. Formula: unreserved = A–Z a–z 0–9 - _ . ~ everything else → %XX per UTF-8 byte unreserved = Characters RFC 3986 guarantees never need escaping, and which must not be escaped. reserved = Delimiters with structural meaning — : / ? # [ ] @ ! $ & ' ( ) * + , ; = — escaped in component mode only. %XX = A percent sign followed by two hexadecimal digits representing one byte. UTF-8 = The encoding applied before percent-escaping, so one character may become several %XX sequences. Worked example — Input: mortgage calculator & rates, Direction: Encode, Scope: Component → mortgage%20calculator%20%26%20rates Each space is a single byte, 0x20, and becomes %20. The ampersand is 0x26 and becomes %26, which is essential: left unescaped inside a query value, it would be read as the start of the next parameter and the value would be truncated at "mortgage calculator". The 27-character input becomes 35 characters. In whole-URL mode the ampersand would have been preserved, which is correct only when encoding an entire URL rather than one value inside it. Questions answered on this page: Q: What is URL encoding? A: URL encoding, also called percent-encoding, replaces characters that are unsafe or reserved in a URL with a percent sign and two hexadecimal digits representing their UTF-8 bytes. Defined in RFC 3986, it lets arbitrary text travel inside a URL without being mistaken for structural syntax such as a parameter separator. Q: What is the difference between encodeURI and encodeURIComponent? A: encodeURIComponent escapes everything except the unreserved set, including & = ? / and #, which is correct for a single value going inside a query parameter. encodeURI leaves those delimiters intact because it expects a complete URL. Using encodeURI on a value that contains an ampersand corrupts the query string. Q: Why does a space become %20 and not a plus sign? A: Both appear, in different contexts. RFC 3986 percent-encoding renders a space as %20 anywhere in a URL. The older application/x-www-form-urlencoded format used by HTML form submissions encodes a space as a plus sign instead. A plus sign inside a path segment therefore means a literal plus; inside a form-encoded query it means a space. Q: Which characters never need encoding? A: The unreserved set: the letters A to Z in both cases, the digits 0 to 9, and the four marks hyphen, underscore, full stop and tilde. RFC 3986 guarantees these are safe everywhere in a URL and specifies that they should not be escaped, because percent-encoding them produces a different but equivalent URL that breaks string comparison and caching. Q: What causes a malformed URI error when decoding? A: A percent sign not followed by two valid hexadecimal digits, such as a bare % in "100% free", or a percent-escape sequence that does not form valid UTF-8. Decoding rejects the whole string rather than guessing. Encoding a literal percent sign as %25 before it enters a URL avoids the problem entirely. Q: Should a URL be encoded twice? A: Only when a complete URL is being carried inside another URL, such as a redirect target in a query parameter. In that case the inner URL is encoded once as a component, and its percent signs become %25 in the outer encoding. Accidental double encoding is a common bug, showing up as visible %2520 sequences in the address bar. Sources: - RFC 3986 — Uniform Resource Identifier (URI): Generic Syntax — IETF — https://www.rfc-editor.org/rfc/rfc3986.html - URL Standard — parsing and percent-encoding — WHATWG — https://url.spec.whatwg.org/ - application/x-www-form-urlencoded serialisation — WHATWG HTML Standard — https://html.spec.whatwg.org/multipage/form-control-infrastructure.html --- ### Hash generator URL: https://truescalers.com/developer-tools/hash-generator Last reviewed: 2026-08-09 A cryptographic hash maps input of any length to a fixed-length digest. SHA-256 always produces 256 bits, written as 64 hexadecimal characters, and the SHA-256 digest of "abc" is ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad. Changing one input bit changes roughly half the output bits, an effect known as the avalanche property. Formula: digest = SHA-n(message); |digest| = n bits = n ÷ 4 hex characters message = The input, of any length, hashed as UTF-8 bytes for text or as raw bytes for a file. n = The digest width in bits — 160 for SHA-1, 256, 384 or 512 for the SHA-2 family. digest = The fixed-length output, rendered here as lowercase hexadecimal. avalanche = The property that a one-bit input change flips about half the output bits, making digests uncorrelated. Worked example — Input: abc, Algorithm: SHA-256 → ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad The 3-byte input "abc" is padded and processed through 64 rounds of the SHA-256 compression function, producing 256 bits of output written as 64 hexadecimal characters. This value is the published test vector in FIPS 180-4, so it can be checked against the standard itself. Changing the input to "abd" produces a completely unrelated digest with roughly 128 of the 256 bits flipped, despite differing by a single bit of input. Questions answered on this page: Q: What is a cryptographic hash function? A: A cryptographic hash maps input of any size to a fixed-size digest with three properties: it is infeasible to recover the input from the digest, infeasible to find a second input with the same digest, and infeasible to find any two inputs that collide. Those properties make digests usable as compact, verifiable fingerprints of data. Q: Which hash algorithm should be used? A: SHA-256 is the current default for integrity checking, digital signatures and certificate fingerprints. SHA-512 offers a wider digest and is actually faster on 64-bit hardware. SHA-384 appears in TLS cipher suites. SHA-1 is broken for security purposes and should be used only to verify a legacy checksum that already exists. Q: Why is SHA-1 considered broken? A: The SHAttered research published in 2017 produced two different PDF files with an identical SHA-1 digest, demonstrating a practical collision. Cost has fallen sharply since. A collision means an attacker can substitute one document for another while the checksum still matches, which defeats the entire purpose of the digest for security use. Q: Can a hash be reversed to recover the original text? A: Not by computation. Hashing destroys information — any length of input maps to a fixed output — so there is nothing to invert. Short or common inputs can still be found by brute force or rainbow table, which is why the digest of a common password reveals it instantly. Salting defeats precomputed tables. Q: Should passwords be stored as SHA-256 hashes? A: No. SHA-256 is designed to be fast, and modern hardware computes billions of digests per second, so a stolen database of SHA-256 password hashes falls quickly to brute force. Password storage needs a deliberately slow, salted, memory-hard function — Argon2id is the current recommendation, with bcrypt and scrypt acceptable alternatives. Q: How do you verify a downloaded file with a checksum? A: Choose the file here, select the algorithm the publisher used, and compare the resulting digest character by character against the published value. An exact match confirms the file arrived intact and unmodified. Any difference at all means the file is corrupt or has been tampered with, and it should not be run. Q: Is the text or file uploaded to generate a hash? A: No. Hashing uses the Web Crypto API's digest function, implemented natively in the browser and executed in this page. A file is read from local disk into memory and hashed there. Nothing is transmitted, and this site has no server-side code capable of receiving data, so hashing a private document is safe. Sources: - FIPS 180-4 — Secure Hash Standard — US National Institute of Standards and Technology — https://csrc.nist.gov/pubs/fips/180-4/upd1/final - SHAttered — the first practical SHA-1 collision — CWI Amsterdam and Google Research — https://shattered.io/ - Password Storage Cheat Sheet — OWASP — https://cheatsheetseries.owasp.org/cheatsheets/Password_Storage_Cheat_Sheet.html --- ### Regex tester URL: https://truescalers.com/developer-tools/regex-tester Last reviewed: 2026-08-09 A regular expression tester runs a pattern against sample text and shows every match, its offset, and the contents of each capture group. The pattern /(\w+)@(\w+\.\w+)/ applied to "ada@example.com" produces 1 match with 2 capture groups: "ada" and "example.com". Matching here uses the browser's own JavaScript regular-expression engine. Formula: new RegExp(pattern, flags).exec(subject) repeatedly until null pattern = The regular expression source, without the enclosing slashes. flags = Modifiers: g global, i ignore case, m multiline, s dot-matches-newline, u unicode. capture group = A parenthesised sub-pattern whose matched text is reported separately, numbered from 1. lastIndex = The engine's position marker, advanced after each match so iteration progresses. Worked example — Pattern: (\w+)@(\w+\.\w+), Flags: gm, Test string: Contact: ada@example.com, grace@example.org → 2 matches, each with 2 capture groups The pattern looks for one or more word characters, an at sign, then a domain of word characters, a dot and more word characters. Against the sample it finds "ada@example.com" at offset 9 and "grace@example.org" at offset 26. Each match yields group 1 as the local part, "ada" and "grace", and group 2 as the domain, "example.com" and "example.org". The g flag is what makes the engine continue past the first match rather than stopping. Questions answered on this page: Q: What does the g flag do in a regular expression? A: The global flag makes the engine find every match rather than stopping at the first. Without it, exec returns only the first match and replace substitutes only one occurrence. This tester forces the global flag on so the full match list can be shown, which is why the count may exceed what the same pattern returns without it in your own code. Q: What is a capture group? A: A capture group is a parenthesised part of a pattern whose matched text is reported separately, numbered from 1 in the order the opening parentheses appear. Named groups use the syntax (?...) and are reported by name as well. Non-capturing groups, written (?:...), group for structure without producing a result. Q: What is the difference between greedy and lazy matching? A: Greedy quantifiers such as * and + take as much text as possible and then give characters back until the rest of the pattern fits. Lazy quantifiers, written *? and +?, take as little as possible and expand only as needed. Matching HTML tags with <.*> greedily swallows everything to the last angle bracket; <.*?> stops at the first. Q: What is catastrophic backtracking? A: Nested quantifiers over overlapping alternatives, such as (a+)+b, can force the engine to try exponentially many ways to split the input before concluding there is no match. A few dozen characters can then hang a process for minutes. Because this is a real denial-of-service vector on servers, patterns applied to user input should avoid nested quantifiers. Q: Should regular expressions be used to validate email addresses? A: Only loosely. The RFC 5322 grammar is far more permissive than most people expect, and a fully conforming pattern runs to hundreds of characters while still rejecting valid addresses. Checking for a single at sign with something before and after it, then sending a confirmation email, is more reliable than any pattern. Q: Do regular expressions work the same in every language? A: No. This tester uses the JavaScript engine, whose syntax is close to PCRE but not identical. JavaScript gained lookbehind only in ES2018, has no possessive quantifiers or atomic groups, and requires the u flag for correct Unicode property handling. Python, Java, Go and PCRE all differ in named-group syntax and available features. Q: Is the test text sent anywhere? A: No. Both the pattern and the subject text stay in this page, and matching runs on the browser's own regular-expression engine. Nothing is transmitted, logged or stored, and this site has no server-side code that could receive it, so testing a pattern against real log output or customer data is safe. Sources: - ECMAScript specification — RegExp objects — Ecma International, TC39 — https://tc39.es/ecma262/multipage/text-processing.html - Regular expressions — syntax reference — Mozilla Developer Network — https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_expressions - Regular expression Denial of Service (ReDoS) — OWASP — https://owasp.org/www-community/attacks/Regular_expression_Denial_of_Service_-_ReDoS --- ## Text tools TrueScalers publishes two text tools: a word counter reporting words, characters, sentences, paragraphs and reading time, and a case converter supporting eleven letter cases including title case, camelCase and snake_case. Both process text inside the browser, so pasted documents are never uploaded. ### Word counter URL: https://truescalers.com/text-tools/word-counter Last reviewed: 2026-08-09 A word counter reports the number of words, characters, sentences and paragraphs in a passage of text. A word is any run of characters separated by whitespace. Reading time is estimated at 238 words per minute for silent adult reading and 150 words per minute for spoken delivery, so a 1,000-word article takes about 4 minutes to read and 7 minutes to say aloud. Formula: words = whitespace-separated tokens reading minutes = words ÷ 238 150 = Typical spoken delivery rate in words per minute for presentations. 238 = Mean silent reading rate in words per minute for adults reading non-fiction English. words = Runs of non-whitespace characters, counted after trimming leading and trailing space. characters = Unicode code points, so an emoji or an accented letter counts as one character. sentences = Runs of text terminated by a full stop, question mark or exclamation mark, with repeated terminators collapsed. Worked example — Text: "The quick brown fox. It jumped over the lazy dog!" → 10 words, 49 characters, 2 sentences Splitting on whitespace gives ten tokens: The, quick, brown, fox., It, jumped, over, the, lazy, dog!. Counting every code point including spaces gives 49 characters, and 40 with spaces removed. Two terminators — the full stop and the exclamation mark — mark two sentences. At 238 words per minute, reading time rounds up to the one-minute floor. Questions answered on this page: Q: How is a word counted? A: A word is any unbroken run of characters bounded by whitespace. Hyphenated compounds such as "well-known" count as one word, and a number such as "1,250" also counts as one. This matches the counting method used by Microsoft Word and Google Docs, so results align with the tools most word limits are checked in. Q: How many pages is 1,000 words? A: Roughly two pages double-spaced or one page single-spaced, in 12-point Times New Roman with one-inch margins — the standard academic format. A single-spaced page holds about 500 words and a double-spaced page about 250. Font, spacing and margins change the figure substantially, so a page count is always an approximation. Q: How long does it take to read 1,000 words? A: About four minutes at the adult average silent reading rate of 238 words per minute. Reading aloud is considerably slower, at roughly seven minutes for the same passage at a typical presentation pace of 150 words per minute. Dense technical or unfamiliar material can halve both figures. Q: What is the difference between characters with and without spaces? A: Characters with spaces counts every character including spaces, tabs and line breaks. Characters without spaces counts only visible glyphs. Publishing and translation contracts frequently price by characters without spaces, while social platforms count characters with spaces — X allows 280 including spaces, and a meta description should stay under about 155. Q: How many words should an article be for search ranking? A: There is no threshold length that ranks. Length correlates with performance only because thorough answers tend to be longer, not because length itself is a ranking factor. What matters is covering the query completely and being extractable. In practice, 1,200 to 2,000 words is common for competitive informational queries, and far shorter is fine for a direct factual answer. Q: Is my text sent anywhere when I use this counter? A: No. All counting happens inside your browser using JavaScript running on this page. The text is never transmitted, logged or stored, and this site has no server-side code capable of receiving it. Closing the tab discards it entirely, which makes the tool safe for drafts, contracts and confidential material. Sources: - How many words do we read per minute? A review and meta-analysis of reading rate — Brysbaert, Journal of Memory and Language, 2019 — https://www.sciencedirect.com/science/article/pii/S0749596X19300786 - Unicode Standard Annex 29 — text segmentation — Unicode Consortium — https://unicode.org/reports/tr29/ - Plain language guidelines — sentence and paragraph length — US Plain Language Action and Information Network — https://www.plainlanguage.gov/guidelines/ --- ### Case converter URL: https://truescalers.com/text-tools/case-converter Last reviewed: 2026-08-09 A case converter changes the capitalisation of text without altering its words, and this one supports 11 cases. Title Case capitalises each significant word while leaving articles, short prepositions and conjunctions lowercase, so "the lord of the rings" becomes "The Lord of the Rings". Programming cases join words instead: camelCase, PascalCase, snake_case, kebab-case and CONSTANT_CASE. Formula: tokenise on word boundaries → apply the target case rule → rejoin with the target separator tokenise = Split on non-alphanumeric characters and at lowercase-to-uppercase transitions, so existing camelCase is recognised. case rule = The capitalisation applied to each token, which differs by target case. separator = Empty for camelCase and PascalCase, underscore for snake_case, hyphen for kebab-case. Worked example — Text: the quick brown fox jumps over the lazy dog, Convert to: Title Case → The Quick Brown Fox Jumps Over the Lazy Dog All 9 words are capitalised except recognised minor words — articles, coordinating conjunctions and short prepositions. The word "the" appears twice: the 1st is capitalised because it opens the title, and the 2nd stays lowercase because it sits mid-title. The word "over" is capitalised because it is not on the minor-word list. The final word is always capitalised regardless of its class. Converting the same text to camelCase instead gives theQuickBrownFoxJumpsOverTheLazyDog. Questions answered on this page: Q: What is title case and which words stay lowercase? A: Title case capitalises the first letter of each significant word. Articles (a, an, the), coordinating conjunctions (and, but, or, nor) and short prepositions (of, in, to, for, on) remain lowercase unless they are the first or last word of the title. Style guides differ on the preposition length cut-off — AP capitalises those of four letters or more. Q: What is the difference between title case and sentence case? A: Title case capitalises most words in the string. Sentence case capitalises only the first word of each sentence and any proper nouns, exactly as ordinary prose is written. Most modern publications and product interfaces have moved to sentence case for headings, on the grounds that it reads faster and looks less shouty. Q: What is camelCase and where is it used? A: camelCase joins words with no separator and capitalises every word except the first, as in myVariableName. It is the conventional identifier style for variables and functions in JavaScript, Java, Swift and C#. PascalCase, also called UpperCamelCase, capitalises the first word too and is conventionally reserved for classes and types. Q: When should snake_case or kebab-case be used? A: snake_case, with underscores, is the convention for variables and functions in Python, Ruby and SQL column names. kebab-case, with hyphens, is standard for URLs, CSS class names and HTML attributes, because underscores are harder to see under a hyperlink underline and hyphens are treated as word separators by search engines. Q: What is CONSTANT_CASE? A: CONSTANT_CASE, also called SCREAMING_SNAKE_CASE, uses all uppercase letters joined by underscores, as in MAX_RETRY_COUNT. Nearly every language convention reserves it for compile-time constants and environment variables, which is why an all-caps identifier signals to a reader that the value is fixed and defined elsewhere. Q: Does converting case affect accented or non-Latin characters? A: Conversion here is Unicode-aware, so accented Latin characters convert correctly — é becomes É in uppercase, and ß uppercases to SS. Scripts without letter case, including Chinese, Japanese, Arabic and Hebrew, pass through unchanged, which is the correct behaviour since the concept of case does not apply to any of them. Sources: - Unicode Standard Annex 21 — case mappings — Unicode Consortium — https://www.unicode.org/reports/tr21/ - Capitalization in titles and headings — The Chicago Manual of Style — https://www.chicagomanualofstyle.org/ - Plain language guidelines — headings and readability — US Plain Language Action and Information Network — https://www.plainlanguage.gov/guidelines/ ---