Which levels do the maths simulations cover?

GCSE (straight lines, quadratics, transformations, circle theorems, probability), A-Level (calculus, distributions, numerical methods) and first-year university or Further Maths (complex numbers, matrices, Taylor and Fourier series).

Are the numbers exact?

Readouts are computed directly from the formulas, to the decimal places shown, and checked against independent calculations. Sampling experiments are random on purpose, so their results wobble around the exact probability.

Do they work on a phone?

Yes. Everything runs in the browser on phones, tablets and laptops, with touch dragging and full keyboard control.

Maths Simulations

13 interactive maths simulations from GCSE to university: graphs you can drag, experiments you can run, and the numbers behind them.

GCSE

Straight lines: y = mx + c

Two points make one line. Which?

Quadratic graphs: roots and vertex

Where does the parabola cross?

Graph transformations

Which way does f(x + 2) move?

Circle theorems

Drag the points. The angles obey.

Probability experiments

Roll it 10 times or 10 000 times

A-Level

Differentiation from first principles

Shrink h and watch the chord turn

Integration as the area under a curve

More strips, less error. How much less?

Normal and binomial distributions

Shade the area, read the probability

Numerical methods: Newton-Raphson, iteration, bisection

Watch the digits double

University

Complex numbers on the Argand diagram

Why does multiplying by i turn 90°?

Matrices as transformations

Watch a matrix bend the whole grid

Taylor and Maclaurin series

How many terms until it fits?

Fourier series

Build a square wave out of sine waves

More simulations: Physics and Chemistry Simulations, Unit Circle, Graphing Calculator

About this tool

Maths Simulations is a free set of 13 interactive maths visualisers, grouped by level. GCSE: straight lines, quadratics, graph transformations, circle theorems and probability experiments. A-Level: differentiation from first principles, integration as area, the normal and binomial distributions, and numerical methods. University: complex numbers on the Argand diagram, matrices as transformations, Taylor series and Fourier series. Drag the graphs, run the experiments and read the exact numbers; every result is checked against an independent calculation.

Tips

Change one thing at a time and watch which readout moves.
For trig, the Unit Circle shows exact values of sin, cos and tan at the special angles.
Use the Graph Plotter when you want to draw any function of your own.

FAQ

Which levels do the maths simulations cover?: GCSE (straight lines, quadratics, transformations, circle theorems, probability), A-Level (calculus, distributions, numerical methods) and first-year university or Further Maths (complex numbers, matrices, Taylor and Fourier series).
Are the numbers exact?: Readouts are computed directly from the formulas, to the decimal places shown, and checked against independent calculations. Sampling experiments are random on purpose, so their results wobble around the exact probability.
Do they work on a phone?: Yes. Everything runs in the browser on phones, tablets and laptops, with touch dragging and full keyboard control.