PPolySim OS

Root Finding

Solve f(x) = 0, one geometric step at a time. Watch Newton–Raphson ride the tangent, bisection squeeze a bracket, and the secant method draw chords to the crossing.

Root Finding StudioLive

Controls

Function

Method

Solve f(x) = 0. Watch the method step toward the root — Newton rides the tangent, bisection halves the bracket, secant draws chords.

Presets

▶ Run in Python

Data Inspector

MethodNewton–Raphson
Step0/4
Estimate x2.500000
|f(x)|4.25e+0
Iters to 1e-64
Order≈ 2 (quadratic)

Governing equation

x02.500000
Reading this result: Newton–Raphson converged to x ≈ 2.500000 in 4 iterations (|f(x)| < 1e-6). Near a simple root Newton roughly doubles the number of correct digits each step (quadratic convergence).

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How it works

Root finding locates where a function crosses zero. Newton–Raphson follows the tangent line at the current guess down to the x-axis and converges quadratically near a simple root, but a small derivative or a poor start can send it flying. Bisection needs only a sign change on [a, b] and halves the bracket every step — slow but guaranteed. The secant method replaces Newton's derivative with a finite-difference slope through the last two points, converging superlinearly (order ≈ 1.618) with no calculus required. Pick a preset function, choose a method, and scrub the Step slider to see each iterate.

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Frequently asked questions

Is this Newton bisection root finding tool really free?
Yes. Root Finding 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.