Newton’s Method Calculator (Free, with Iteration Table)
Use this free Newton’s method calculator to approximate a root of a function from a starting guess. It shows every iteration, the converged root, and a graph.
How Newton’s method works
Each step follows the tangent line to a better estimate: xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ). It converges quickly when the guess is near a root.
Original price was: $109.99.$54.99Current price is: $54.99.
How to use it
- Enter f(x), a starting value, and the number of iterations.
- Press Run iterations.
Related: the Equation Solver and the Derivative Calculator.
Frequently asked questions
Why does it need a starting guess?
Newton’s method refines an existing estimate; a guess near the root converges fastest.
Original price was: $109.99.$54.99Current price is: $54.99.
When can it fail?
If the derivative is zero at a step or the guess is far from any root, it may stall or diverge — try another start.
Original price was: $109.99.$54.99Current price is: $54.99.
Does it show each step?
Yes — the iteration table lists xₙ, f(xₙ), and the next estimate.
Original price was: $27.99.$17.99Current price is: $17.99.
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