Newton Raphson Method Calculator
Work out newton raphson method instantly with clear inputs, formula shown and shareable results.
About Newton Raphson Method Calculator
Newton-Raphson follows the tangent line to its x-intercept: xₙ₊₁ = xₙ − f(xₙ)/f'(xₙ). Near a simple root it converges quadratically, roughly doubling the number of correct digits each step.
Formula
Newton-Raphson
xₙ₊₁ = xₙ − f(xₙ) / f'(xₙ)
Worked example
With the default values below, Newton Raphson Method Calculator returns Root found of 1.4142135624. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Polynomial coefficients, highest power first
- 1, 0, -2
- Starting guess
- 1.5
- Iterationsaccepts 1–100
- 6
Results
- Root found
- 1.4142135624
- f(root) — should be near zero
- 0.000000000000
- Iterations used
- 5
- f' at the root
- 2.82842712
Step by step
- 1Values used
- 2Newton-Raphson
- 3Root found= 1.4142135624
- 4f(root) — should be near zero= -0.000000000000
- 5Iterations used= 5
- 6f' at the root= 2.82842712
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 12 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Solve x² − 2 = 0 from x = 1.5.
It converges to √2 = 1.4142136 within about four iterations.
When does it fail?
At a zero derivative, at an inflection near the root, or from a poor starting guess — then it can cycle or diverge.