Newton Raphson Calculator
One Newton step at a time, with convergence check.
Enter your values
Enter the current estimate xₙ you are working with.
Enter the f(xₙ) you are working with.
Enter the f′(xₙ) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | One Newton step at a time, with convergence check. |
|---|---|
| Category | Math |
| Inputs needed | Current estimate xₙ, f(xₙ), f′(xₙ) |
| Main output | Next estimate xₙ₊₁ |
| Formula | xₙ₊₁ = xₙ − f(xₙ) ÷ f′(xₙ) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Current estimate xₙ
- Enter the current estimate xₙ you are working with.
- f(xₙ)
- Enter the f(xₙ) you are working with.
- f′(xₙ)
- Enter the f′(xₙ) you are working with.
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.
What do I need to enter into the Newton Raphson Calculator?
Just 3 values: current estimate xₙ, f(xₙ), f′(xₙ). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Newton Raphson Calculator work out the 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. It applies the formula xₙ₊₁ = xₙ − f(xₙ) ÷ f′(xₙ) and shows the working so you can check each step by hand.
Is the Newton Raphson Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.