Gradient Descent Playground
Gradient Descent Playground animates discrete steps on three cost curves and illustrates learning rates and stationary points in your browser.
xₖ₊₁ = xₖ − ηJ′(xₖ)
Position · iteration 0
Cost J(x)
Gradient J′(x)
Drag the curve to change the starting point. Gold links show discrete steps, not continuous downhill motion.
At a glance
- Accepts
- Three objectives, starting point and learning rate
- Outputs
- Ball trajectory, cost history, gradients and next-step calculations
- Where it runs
- Entirely in your browser, on your device
- What leaves your device
- No calculation inputs are uploaded; standard site usage analytics still apply
- Limits
- One-dimensional presets; up to 40 iterations; stops before numerical overflow; plot window is finite
- Account
- Not required - there is no sign-up
- Price
- Free, with no watermark and no usage cap
- Made by
- Visrut
- Last updated
- 14 October 2026
What to notice
Gradient descent repeatedly takes xₖ₊₁ = xₖ − ηJ′(xₖ). A negative gradient moves right; a positive gradient moves left. The learning rate η controls the step size.
For J(x) = x², rates between 0 and 1 converge. At η = 1 the point oscillates without shrinking; rates above 1 diverge unless started exactly at zero. For other curves, a safe rate depends on curvature and location.
A zero derivative can also occur at a maximum: starting at zero in the two-valley preset stays there. The algorithm does not know whether a stationary point is a minimum. The simulation stops before numerical overflow, and the displayed curve has a finite window.
Reference: gradient descent intuitionFrequently asked questions
Are these symbolic calculators?
These tools teach through supported function presets, exact derivatives and antiderivatives where supplied, and labelled numerical approximations. They do not evaluate arbitrary expressions.
Do calculations leave my device?
All graphs and calculations run locally in your browser. No account or external calculation service is required.