Direction Field
See the shape of an ODE before you solve it. Type dy/dx = f(x,y) to draw its slope field, then click anywhere to trace a solution curve through that point.
Direction Field / Slope FieldLive
dy/dx = f(x, y) · drag the start point
Controls
Data Inspector
Equationdy/dx = f(x,y)
Curves1
IntegratorRK2
Governing equation
Reading this result: Every tick shows the slope dy/dx = f(x,y) at that point; drag the start point and RK2 rethreads the solution curve live, always staying tangent to the arrows. That start point alone picks which one curve you get — click elsewhere to pin extra curves for comparison.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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How it works
A direction field draws a short line at each point with slope f(x,y), revealing the family of solutions to a first-order ODE. Clicking seeds a numerically-integrated solution curve, so you can watch how initial conditions pick out one trajectory.
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Frequently asked questions
Is this slope field direction field tool really free?▾
Yes. Direction Field 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.