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Newton's method calculator

Find a root of f(x) = 0 with Newton's method: x_{n+1} = x_n − f(x_n) / f′(x_n). Enter a function, a starting guess, a tolerance and a maximum number of iterations; the tool differentiates f symbolically and shows the full iteration table converging to the root.

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Newton's method calculator works straight from this page — free, instant, nothing to install. It covers x_{n+1} = x_n − f(x_n) / f′(x_n). Enter a function, a starting guess, a tolerance and a maximum number of iterations; the tool differentiates f symbolically and shows the full iteration table converging to the root — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Newton's method calculator do?

Find a root of f(x) = 0 with Newton's method: x_{n+1} = x_n − f(x_n) / f′(x_n). Enter a function, a starting guess, a tolerance and a maximum number of iterations; the tool differentiates f symbolically and shows the full iteration table converging to the root.

What does a concrete case look like?

x² − 2, x₀ = 1 → 1,5 → 1,41667 → 1,414216 = √2 — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in x_{n+1} = x_n − f(x_n) / f′(x_n). Enter a function, a starting guess, a tolerance and a maximum number of iterations; the tool differentiates f symbolically and shows the full iteration table converging to the root. Change any of them and the output follows immediately.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Newton's method calculator different from Euler's Method Calculator?

They sit next to each other but answer different questions: Euler's Method Calculator is the one to open when you need it to steps through Euler's method one row at a time and — the whole point of the method — shows how far it drifts from the exact solution. Give the exact y(x) and the error column appears; halve the step and watch the error halve with it. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Runge-Kutta (RK4) Method Calculator is the closest one after this: Shows the four stage slopes k₁ to k₄ at every step and how the 1-2-2-1 weighting cancels the error through h⁴. Halve the step and the error drops about sixteenfold — the measured order is printed so you can watch it approach 4.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

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