Parametric Grapher
Let a point move by x(t) and y(t) and it draws a curve — roses, spirals, Lissajous figures, even a heart. Type your own and watch it trace.
Parametric Curve GrapherLive
x(t), y(t) traced over time
Controls
Data Inspector
x(t)param
y(t)param
t range0…6.3
Governing equation
Reading this result: x(t)=cos(3*t), y(t)=sin(4*t) are swept over t from 0 to 6.3 — a full 2π range, so periodic curves close into a complete loop.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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How it works
Parametric equations describe a curve by the position of a moving point over a parameter t. This grapher parses x(t) and y(t) with PolySim's symbolic engine and animates the trace, making periodic and self-intersecting curves easy to explore.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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Frequently asked questions
Is this parametric curve grapher tool really free?▾
Yes. Parametric Grapher 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.