Math Calculators

Four Tools, Four Different Jobs

This section is deliberately small. It holds the four calculators that do genuine mathematical work rather than applying a formula to everyday quantities, and they belong to fields that rarely overlap.

The distinction is worth stating plainly because the two are sometimes confused by the shape of the input. A single row of numbers can be typed into either, and they will do entirely different things with it: one summarises the values, the other treats them as a vector to be transformed.

Descriptive Statistics in One Sentence

Descriptive statistics reduce a set of observations to a few numbers that stand in for the whole. The useful part is knowing which summary to trust: the mean uses every value and is dragged by extremes, the median ignores magnitude and resists them, and the mode is the only one that works on categories rather than numbers. When those three disagree, the disagreement is itself informative about the shape of the data.

Linear Algebra in One Sentence

A matrix is a transformation written as a grid, and the operations describe what that transformation does. The determinant says whether it can be undone, the inverse undoes it, the rank counts how much independent information it carries, and solving AX = B answers a system of linear equations in a single step. Most errors in this area are dimension errors rather than arithmetic ones, which is why the matrix page leads with the shape rules.

Math That Lives in Other Sections

Several calculations that are unambiguously mathematical sit elsewhere on the site, because they are organised by what people are trying to do rather than by subject.

• Percentage calculator — percentage of, increase, decrease, and reverse percentages
• GPA calculator and GPA to percentage — weighted averages applied to grades
• Unit conversion — scaling between measurement systems
• Time calculator — arithmetic in base 60 rather than base 10
• Math formula library — the formulas themselves, for when you want to work it by hand

If you arrived looking for one of those, the links above are faster than the tools on this page.

Where Floating-Point Arithmetic Shows Through

Both tools compute in the browser using standard double-precision arithmetic, and there are two places where that becomes visible rather than invisible.

The first is harmless. Multiplying a matrix by its own inverse should return the identity, and it will — but the zeros may appear as values like 0.0000000000000002 rather than exactly 0. That is rounding at the seventeenth significant figure, not an error.

The second is not harmless. When a determinant sits very close to zero, the inverse divides by that tiny number and produces enormous entries. Such a matrix is described as ill-conditioned: a change in the fourth decimal place of an input can move the output by orders of magnitude. If your determinant is near zero, treat the inverse as an indication rather than an answer.

Statistical results carry a different caveat entirely. They describe exactly the numbers you entered and say nothing about whether those numbers were collected well. No summary statistic can detect a biased sample, and a precise mean of unrepresentative data is precisely wrong.

Verification and Review Date

Matrix results are checked by multiplying inverses back to the identity and by confirming products against hand-computed entries; statistical measures are checked against sets whose mean, median, spread and standard deviation were worked out by hand first. Both calculators were last reviewed on 27 August 2026. Our about page describes how tools on this site are built and verified.