About MathTools

MathTools is a collection of more than twenty small calculators for everyday math — from fractions and percentages to matrices, eigenvalues and step-by-step calculus. Each tool does one job and lays out the full working instead of just the final number, and many topics come with randomly generated practice exercises for training on your own.

Exact where it counts

Most tools compute with exact fractions rather than decimals. 0.75 stays 3/4 the whole way through, so rounding never creeps in. The inverse of [[4,7],[2,6]] comes out as 3/5, −7/10, −1/5, 2/5 rather than 0.6 and −0.7. The fractions run on big integers, so large factorials don't overflow either.

Some results are irrational by nature — singular values, plenty of eigenvalues, the sine of a random angle. There the tool switches to a numerical method and says so, instead of dressing up an approximation as exact.

See the working

Every calculation comes with a worked solution. The matrix tools show the augmented matrix after each row operation; the arithmetic ones go term by term — and many tools draw the result as well: lines, parabolas, histograms or the shaded area under an integral. Steps are numbered, so you can follow the method or check the result yourself.

Find the right tool

• Algebra — matrix inversion, determinant, matrix arithmetic & powers, linear systems, quadratic equations, completing the square, equations of a line, polynomial division, polynomial factoring, eigenvalues & eigenvectors, diagonalization, SVD.
• Probability — combinatorics (nPr, nCr, factorials), the binomial distribution, descriptive statistics (mean, median, mode, variance, standard deviation) and the normal distribution with z-scores & percentiles.
• Analysis — polynomial derivatives & integrals, an interactive triangle solver, the unit circle, degrees & radians, arithmetic & geometric sequences, logarithms and the Pythagorean theorem with exact radicals.
• Number Systems — convert and calculate in any base from 2 to 36, exact fraction arithmetic, exponents, gcd & lcm, percentages, ratios, prime factorization and scientific notation.
• Everyday Math — compound interest with schedules, discounts (including successive ones), tips & bill splitting, and unit conversion with exact international factors.

Under the hood

MathTools runs on Nuxt and Nuxt UI. The actual math lives in small TypeScript modules, each with its own unit tests, so the logic can be checked apart from the interface.

Tested, not hoped for

The math behind every tool lives in small, pure TypeScript modules — and each one ships with its own unit tests. More than 500 Vitest tests check exact fraction results, edge cases like singular matrices, division by zero and empty input, and that every tool actually produces its step-by-step working.

Vibe coded

Honestly? This site is vibe coded: a human had the ideas, picked the tools and made the calls, and an AI wrote most of the code, copy and translations. But vibes don't guarantee correctness — so every bit of math is pinned down by the 500+ unit tests above, not by confidence.