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CalcWorld

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How we calculate

The step-by-step calculators all run on one math engine. It works out the answer and the steps together from the same numbers, so the working shown is the working that produced the result. The engine has unit tests that check its answers and steps against examples worked by hand.

Exact where it can be

Fractions are kept as whole-number numerators and denominators and simplified with the greatest common divisor, so 1/3 stays 1/3 instead of becoming 0.3333. Decimals are only rounded for display.

Rounding

Results are shown to at most six decimal places with trailing zeros removed. Where a step uses a rounded value, the final answer is still calculated from the unrounded one.

Statistics conventions

Standard deviation and variance are given for both a sample (dividing by n − 1) and a population (dividing by n). Quartiles use the median-of-halves method taught in most school courses, and the page says so, because other methods give slightly different values. Percentiles use linear interpolation between the two closest ranks.

Older calculators

Calculators that do not yet show numbered steps explain what they calculate in the text under the tool, in most cases with a worked example you can check by hand.

Where the calculation happens

In your browser. The page downloads the calculator once and does the work on your device, so results appear as you type and your inputs are not sent to us. The step-by-step calculators keep your inputs in the page address so that you can share an example. Those addresses are marked so that search engines do not index them.

What a step-by-step calculator page shows

  • The answer, then numbered steps for the exact numbers you entered.
  • The formula, typeset the way it appears in a textbook.
  • A worked example and a practice question, both solved by the same engine as the calculator.
  • The textbook section or reference the method was checked against, with the date it was checked.
  • The date the page was last updated.

There are 17 of these so far:

What the other calculator pages show

The remaining calculators come from the earlier version of the site. Each one is covered by automated tests that load its script and run its buttons, and the text under the tool explains what it calculates, in most cases with a worked example. The calculators that depend on outside values list where those values come from: the wavelength calculator (speeds of light and sound), the stoichiometry calculator (atomic weights), and the mass and speed, distance and time calculators (unit definitions).

Sources we rely on

Limits

CalcWorld is a study aid. Check the method your course or exam board expects, especially for quartiles, percentiles and rounding, where conventions differ. The finance calculators give estimates for learning and planning, not financial advice.