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Newton's Method Calculator

Approximate a root of f(x) from a starting guess using Newton's method — with the full iteration table, the converged root, and a graph.

xₙ₊₁ = xₙ − f(xₙ) / f′(xₙ)
f(x) x₀ = start x₀ , iterations n

Newton's method refines a root with xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ). Pick a starting guess near the root.

Results

Approximate root
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Root
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f(root)
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Iterations used
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Iterations

Graph

f(x)root

Step-by-step