Maths Tools

Solve equations, fractions, triangles and statistics with exact answers and the working shown — from BODMAS to matrices, all in your browser. Learn more

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BODMAS/BIDMAS Step-by-Step Solver

Every order-of-operations step, shown one at a time.
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Complex Number Calculator

Arithmetic and powers, in a + bi and polar form, plotted.
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Fraction Calculator

Mixed numbers, simplified answers and the working.
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GCD/LCM Calculator

HCF and LCM of several numbers, with prime factors.
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Matrix Calculator

Up to 4×4: multiply, determinant, inverse, in exact fractions.
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Modular Arithmetic Calculator

Mod, modular powers and inverses, with Euclid’s working.
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Number Sequence Pattern Solver

Find the nth term, next terms and difference table.
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Percentage Change Calculator

% change, reverse percentages and percentage points.
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Permutations & Combinations

nPr and nCr, with or without repeats, exact.
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Pi Explorer

Up to 100,000 digits, plus a birthday search.
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Prime Number Checker

Is it prime? Factors, and the primes either side.
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Quadratic Equation Solver

Exact surd roots, vertex, factorised form and graph.
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Random Number Generator

Up to 1,000 fair random numbers, with or without repeats.
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Scientific Calculator

Type or tap: trig, logs, powers, memory and history.
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Standard Form/Scientific Notation

Standard form, E and engineering notation, sig figs.
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Statistics Calculator

Averages, quartiles, standard deviation and a box plot.
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Triangle Solver

Any three sides or angles: SSS, SAS, ASA and SSA.
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Vector Calculator

2D or 3D: dot, cross, angle, unit vector, projection.

Free online maths tools that show their working

Whether you're checking homework, revising for GCSE or A level, or just need an answer you can trust, these maths tools give exact results and explain how they got there. The BODMAS Step-by-Step Solver works through a sum one operation at a time, the Fraction Calculator handles mixed numbers and shows each step, and the Quadratic Equation Solver gives roots as simplified surds, such as (3 ± √5)/2, along with the factorised form, vertex and a graph. For everything else there's a full Scientific Calculator that you can type into or tap, with degrees or radians and a history of your answers.

Tools for algebra and geometry include the Number Sequence Pattern Solver, which finds the nth term of linear, quadratic and cubic sequences, the Triangle Solver, which handles any three sides or angles including the ambiguous case, and vector, matrix and complex number calculators that keep answers as exact fractions where they can. For data, the Statistics Calculator gives averages, quartiles and both kinds of standard deviation with a box plot, and the Permutations & Combinations tool counts arrangements exactly, however large.

Number lovers can test numbers of up to 40 digits with the Prime Number Checker, find the HCF and LCM with the GCD/LCM Calculator, explore modular arithmetic, or calculate π to 100,000 places with the Pi Explorer and look for their birthday in it. Everything runs in your browser, with nothing sent to a server.

Questions and answers

What's the difference between the Scientific Calculator and the BODMAS Solver?
Both follow the same order of operations, so they always agree on the answer. The Scientific Calculator is for getting answers quickly, with functions such as sin, log and square roots, memory and history. The BODMAS Solver is for learning: it rewrites the sum after each single operation, so you can see exactly why 6 ÷ 2(1 + 2) is 9 and where a mistake crept in.
Should I use sample or population standard deviation?
Use the sample standard deviation, which divides by n − 1, when your numbers are a sample taken from a bigger group, such as 30 pupils' test scores used to describe a whole year group. Use the population figure, dividing by n, only when you have every value in the group. The Statistics Calculator shows both, matching Excel's STDEV.S and STDEV.P.
When do I use permutations rather than combinations?
Use permutations when the order matters, such as first, second and third place or the digits of a PIN, and combinations when it doesn't, such as a lottery line or a hand of cards. Choosing 3 from 10 gives 720 permutations but only 120 combinations, because each group of 3 can be arranged in 6 orders.
Why do the Quadratic and Sequence solvers give fractions and surds instead of decimals?
Exam questions usually want exact answers, and decimals are rounded. The solvers work in exact whole-number arithmetic, so a quadratic's roots come out as (3 ± √5)/2 and the triangular numbers' nth term as (1/2)n² + (1/2)n, with the decimal values shown alongside when you need them.
How is the Random Number Generator different from Math.random?
It uses your browser's cryptographic random generator, the same source used to create security keys, and discards values that would make some numbers slightly more likely than others. That makes every number in your range exactly equally likely, which matters for fair raffles and draws. It can pick up to 1,000 numbers at once, with or without repeats.