Where formulas come from
We use three kinds of methods, and each calculator page states which applies:
- Exact mathematics. Geometry (areas, volumes, the Pythagorean theorem, trigonometry), algebra (Cramer's rule for linear systems), probability (the binomial distribution), fraction arithmetic and calendar arithmetic have exact definitions. We implement them directly.
- Standard financial formulas. Loan payments use the standard fixed-rate amortization formula. Savings projections use compound growth applied period by period. These are the same relationships used in finance textbooks and lender disclosures, though real products can include fees and terms our tools do not model.
- Published reference equations and typical values. Some questions can only be estimated, such as calorie needs, the energy cost of walking, or how much a cubic yard of gravel weighs. For these we use widely cited published equations (for example the Mifflin-St Jeor equation and the ACSM walking equation) or typical industry values, cite them on the page, and make assumed values editable where practical.
Unit conversions use exact definitions: 1 inch = 2.54 cm, 1 foot = 0.3048 m, 1 pound = 0.45359237 kg, 1 US gallon = 3.785411784 litres and 1 mile = 1.609344 km.
How inputs are processed
- Calculations run entirely in your browser; nothing you enter is sent to us.
- Every input is validated. Empty, non-numeric, negative or out-of-range values produce a specific message next to the field instead of a misleading result.
- Inputs are converted to a single internal unit system before calculating, and converted back for display.
- Impossible combinations, for example a right-triangle leg longer than its hypotenuse, are rejected with an explanation.
How rounding works
Calculations use full double-precision arithmetic (about 15-16 significant digits) internally. We round only for display, and the number of decimals shown depends on what the value is used for:
- Currency is shown to the cent. Loan schedules round each payment's interest to the cent as lenders typically do, and the final payment absorbs any remaining difference.
- Countable items you must buy whole (tiles, boxes, bags, blocks, boards, studs) are rounded up to the next whole unit.
- Volumes, weights and lengths are shown to two decimals; time durations to the second or minute as appropriate.
- Fraction results are exact: numerators and denominators are whole numbers (using arbitrary-precision integers) and are simplified only at the end.
How calculators are tested
The calculation logic for every calculator lives in its own module, separate from the page design, and has automated unit tests. Tests check:
- known-answer cases worked independently by hand or from published examples;
- boundary values such as zero, very small and very large numbers;
- invalid and impossible inputs;
- unit conversions in both directions;
- special cases such as zero-interest loans, overnight shifts, leap years, and systems of equations with no or infinitely many solutions.
Automated browser tests also load every calculator page, enter values, and check that results, error messages and the reset button behave correctly on desktop and mobile screen sizes. A calculator is published only when its tests pass.
Financial assumptions
Financial calculators assume fixed interest rates, payments made on schedule and constant rates of return and inflation unless a page says otherwise. Real markets vary, and the order of returns matters when withdrawing money. Results are illustrations for comparing scenarios, not forecasts, offers of credit or financial advice.
Health and fitness assumptions
Health calculators use equations derived from studies of groups of people. They estimate averages and can be off by 10% or more for an individual. Where an equation requires a sex parameter, it reflects the populations the equation was developed from. Results are general information, not medical advice, and are not appropriate for diagnosing or treating any condition.
Construction assumptions
Construction calculators estimate material quantities. Densities, bag yields and waste allowances vary by product and supplier; the values we use are typical figures that you can change. The calculators do not perform structural design, and none of their results should be used to size structural members, reinforcement or footings.
Reporting errors
If you believe a result is wrong, please contact us with the page address, the values you entered and the result you expected. We investigate every report, add a test that reproduces any confirmed error, fix it, and update the calculator's review date.
How calculators are updated
Each calculator page shows the date its formulas and content were last reviewed. We revisit calculators when a referenced standard or equation is revised, when a user reports a problem, or when we improve a feature. Every change runs through the full automated test suite before it is published.