Fourier Series Builder
Add up sine waves and watch them become a square, sawtooth, or triangle wave. This is the Fourier series, built by hand.
Fourier Series BuilderLive
synthesize waves from sinusoids
Controls
Add harmonics and watch sine waves sum into a square, sawtooth, or triangle wave — the Fourier series in action.
Presets
Data Inspector
Wavesquare
Harmonics8
Basissine
Governing equation
Reading this result: Reconstructing the square wave from 8 sine harmonics. More harmonics sharpen the reconstruction and pull it closer to the ideal shape. But at each discontinuity the Gibbs phenomenon leaves a persistent ~9% overshoot spike — adding terms only narrows that ripple, it never removes it, no matter how many harmonics you sum.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
Any periodic wave can be written as a sum of sinusoids. This tool adds harmonics one at a time so you can see the partial sums converge to the target wave — and watch the Gibbs phenomenon ring near the discontinuities of a square wave.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
More Math simulations
Frequently asked questions
Is this Fourier series tool really free?▾
Yes. Fourier Series Builder runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.