How we calculate
Every calculator on smithmetic shows the formula it uses, and this page documents the constants, formulas, and rounding rules behind them. The goal is simple: you should be able to reproduce any result by hand.
Unit conversions
Conversions use the exact, internationally agreed constants rather than rounded approximations:
- Length: 1 inch = 2.54 cm (exact), so 1 foot = 30.48 cm and 1 mile = 1.609344 km (exact).
- Mass: 1 pound = 0.45359237 kg (exact), which gives 1 kg = 2.2046226 lb.
- Temperature: °F = °C × 9/5 + 32, and °C = (°F − 32) × 5/9. The scales meet at −40°.
- Volume: 1 US gallon = 3.785411784 litres (exact).
These definitions come from the international yard-and-pound agreement of 1959 and the SI system. Because they are exact by definition, the only approximation in a conversion is the rounding of the final displayed figure.
Finance calculators
Loan and mortgage payments use the standard amortization formula, M = P · r(1+r)ⁿ / [(1+r)ⁿ − 1], where P is the principal, r is the monthly interest rate, and n is the number of monthly payments. Compound interest uses A = P(1 + r/n)^(nt). These tools calculate principal and interest only; real-world payments may also include taxes, insurance, and fees, which we note on the relevant pages.
Health calculators
Health tools use widely published, standard formulas — for example, BMI = weight(kg) / height(m)², and the Mifflin-St Jeor equation for calorie estimates. These are population-level estimates and screening tools, not diagnoses. They do not account for individual factors like muscle mass, and they are not a substitute for advice from a qualified medical professional.
Rounding
Calculations are performed at full floating-point precision and only the final displayed value is rounded — we never chain rounded intermediate results, which would compound error. Each tool rounds to a sensible number of decimal places for its unit (for example, two decimals for pounds, more for small metric lengths). The conversion tables on each value page show the rounded figures, but the underlying math is exact.
Found an error?
If a result looks wrong, please get in touch with the page and the numbers you entered. Corrections are made quickly, and accuracy reports are always welcome.