How to use the newton's method square root calculator
Approximate a square root with Newton iterations. Enter number, initial guess, iterations in the fields above; the estimate, true square root, absolute error are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- N — Number
- x0 — Initial guess
- k — Iterations
Worked example
With number = 2, initial guess = 1, iterations = 5, the calculator gives estimate ≈ 1.414214; true square root ≈ 1.414214; absolute error ≈ 2.2204 × 10⁻¹⁶.
Frequently asked questions
What is the formula for the newton's method square root calculation?
Estimate = newtonSqrt(N,x0,k). True square root = √(N). Absolute error = abs([Estimate]-[True square root]). Here N is number, x0 is initial guess, k is iterations.
What inputs do I need for the newton's method square root calculator?
You need number, initial guess, iterations. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.