About MathTools

MathTools is a set of small calculators for everyday math. Each one does a single job, like inverting a matrix or solving a quadratic, and lays out the full working instead of just the final number.

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. Steps are numbered, so you can follow the method or check the result yourself.

Find the right tool

• Algebra — matrix inversion, determinant, matrix arithmetic, quadratic equations, eigenvalues & eigenvectors, diagonalization, SVD.
• Probability — combinatorics (nPr, nCr, factorials) and the binomial distribution.
• Analysis — polynomial derivatives & integrals and an interactive triangle solver.
• Number Systems — convert and calculate in any base from 2 to 36.

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. The source is on Forgejo.