Newton's Method Visualizer
Enter a supported function of x and a starting value to follow Newton iterations toward a root.
A QUICK WALKTHROUGH
How to use this tool
- Enter f(x), a finite starting value, and an iteration limit from 1 to 30.
- Run the iterations and inspect each function value, derivative, and next estimate.
- Use the diagram to see the curve, tangent steps, and any reported stopping condition.
A restricted expression language
Supported syntax: x, numbers (including scientific notation), pi, e, parentheses, + − * / ^, and sin, cos, tan, exp, log, sqrt, abs. Implicit multiplication is accepted (2x, 2(x+1)); function names require parentheses. This is parsed locally with explicit rules; arbitrary JavaScript is never executed.
Numerical derivative and stopping
The derivative is estimated with a scale-aware central difference. The run stops on convergence, a near-zero or non-finite derivative, a non-finite/diverging iterate, a detected cycle, or the iteration limit. Numerical results depend on the starting point and finite precision.
Local processing
The expression and all calculations stay in this browser. The chart is a visual aid with an automatically selected finite x-range; values outside the real domain are omitted.
GOOD TO KNOW
Common questions
Does Newton’s method always find a root?
No. It can diverge, cycle, encounter a zero derivative, or converge to a root that depends on the starting value.
Can I enter JavaScript or arbitrary functions?
No. Only the listed mathematical syntax and functions are accepted; the input is parsed and never passed to eval or Function.
Why is the derivative approximate?
This visualizer uses a central finite difference, so it is an estimate and can be sensitive near singularities or at extreme magnitudes.