Newton Raphson Calculator
One Newton step at a time, with convergence check.
Enter your values
ⓘ Live results
Results
- Next estimate xₙ₊₁
- 2.25
- Step size
- 0.25
- Relative change
- 11.111111%
- Converging?
- Yes — step is shrinking
- Estimated correct digits gained
- 0.6
Quick answer
Newton's method improves a root estimate with xₙ₊₁ = xₙ − f(xₙ) ÷ f′(xₙ), roughly doubling the number of correct digits each step.
xₙ₊₁ = xₙ − f(xₙ) ÷ f′(xₙ)
How to use the Newton Raphson Calculator
- 1Enter your current estimate of the root.
- 2Enter the function value and derivative at that point.
- 3Feed the new estimate back in and repeat until the step size is tiny.
Worked example
Using the values the calculator loads with:
Inputs
- Current estimate xₙ2
- f(xₙ)-1
- f′(xₙ)4
Results
- Next estimate xₙ₊₁2.25
- Step size0.25
- Relative change11.111111%
- Converging?Yes — step is shrinking
- Estimated correct digits gained0.6
Frequently asked questions
When does Newton's method fail?
Near a zero derivative, at inflection points, or with a poor starting guess — it can oscillate or shoot off entirely.
How many iterations do I need?
Usually 4 to 6 from a decent start, because the method converges quadratically.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.