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Math tools, steps included

Every result comes with the full working, step by step.

Quadratic Equation Solver Train Exercises

Algebra

Matrices and equations, with every step shown.

Matrix Inversion

Find the inverse of a square matrix

Determinant Calculator

Determinant with every step shown

Matrix Calculator

Add and multiply two matrices

Matrix Power Aⁿ

Raise a square matrix to any integer power

Systems of Linear Equations

Solve Ax = b exactly, with every row operation shown

Quadratic Equation Solver

Exact roots, discriminant and factored form

Completing the Square

Vertex form a(x − h)² + k, vertex & axis of symmetry — exact, with steps

Equation of a Line

Slope, intercepts & y = mx + b from two points or slope + point

Polynomial Division

Long division of polynomials — quotient & remainder with steps

Polynomial Factoring

Factor polynomials up to degree 4 — exact, with every step

Eigenvalues & Eigenvectors

All eigenvalues, exact where possible

Matrix Diagonalization

Write A as P D P⁻¹

Singular Value Decomposition

Factor A into U Σ Vᵀ

Probability

Counting, discrete distributions & descriptive statistics — exact throughout.

Combinatorics

Factorials, permutations (nPr) and combinations (nCr)

Binomial Distribution

Exact PMF, CDF, mean and variance

Descriptive Statistics

Mean, median, mode, variance & standard deviation — exact, with steps

Normal Distribution

Probabilities, z-scores & percentiles for any mean and σ

Analysis

Polynomial calculus and sequences, plus a triangle you can drag.

Derivative & Integral

Differentiate and integrate polynomials

Triangle Solver

Drag the vertices or type the sides and angles

Pythagorean Theorem

Find a missing side or check for a right triangle, exactly

Unit Circle & Trig Values

Exact sin, cos & tan for special angles, numeric otherwise — with steps

Degrees ↔ Radians

Convert angles exactly as fractions of π — with steps

Sequences & Series

Arithmetic & geometric sequences: nth term, partial and infinite sums

Logarithm Calculator

log, ln, log base 2 or any base — exact when possible, with steps

Number Systems

Convert and compute in any base from 2 to 36 — plus exact fraction arithmetic, gcd & lcm, prime factorization & percentages.

Base Converter

Convert and calculate in binary, octal, decimal, hex & more

Fraction Calculator

Add, subtract, multiply and divide fractions exactly

Exponent Calculator

Powers, negative & fractional exponents — exact when possible, with steps

Scientific Notation

Convert and calculate with a × 10ⁿ — exact, with steps

GCD & LCM

The Euclidean algorithm, step by step, for numbers of any size

Percentage Calculator

Percent of a number, percent value & percent change — exact, with steps

Ratio Calculator

Simplify ratios, solve proportions and share amounts — exact, with steps

Prime Factorization

Break any integer into its prime factors — with steps

Roman Numeral Converter

Numbers to roman numerals and back, 1–3999 — greedy steps plus a chart

Everyday Math

Practical math for money and growth — interest and everyday figures, computed exactly.

Compound Interest Calculator

Future value with periodic contributions — exact fractions, every step shown

Discount Calculator

Sale price after successive discounts and optional tax — exact, with steps

Tip Calculator

Tip, total and per-person split of any bill — exact to the cent

Unit Converter

Exact metric-imperial conversion with steps: length, mass, temperature, more

Mortgage Calculator

Monthly payment, total interest and amortization schedule — exact

MathTools

Free online math tools for linear algebra, calculus, probability and number systems — exact fractions where possible, with the full working shown.

Practice Exercises About MathTools