Newton's Method Calculator
Approximate a real root of an equation using Newton–Raphson iteration. Enter a function, its derivative, and a starting value to see every iteration, convergence status, and a graph preview.
Use x as the variable, for example x^3 - x - 2.
Provide an initial guess close to the expected root.
See each Newton step until the chosen tolerance is reached.
| n | xₙ | f(xₙ) | f′(xₙ) | xₙ₊₁ | |Δx| |
|---|
Newton's method uses the tangent line at the current estimate to predict a better root approximation. The process repeats until the change in x or the residual becomes sufficiently small.
Use numbers, x, parentheses, +, −, *, /, and ^. Common functions are also supported: sin(x), cos(x), tan(x), sqrt(x), abs(x), exp(x), log(x), and ln(x). Trigonometric functions use radians.
Newton's method is sensitive to the starting value. It may converge to a different root, fail when the derivative is zero, oscillate, or diverge. Try another initial guess when convergence fails.
What is Newton's method?
Newton's method is an iterative numerical technique for approximating roots of equations by repeatedly using tangent-line intersections.
Why do I need the derivative?
The derivative gives the tangent slope used to calculate the next approximation.
What happens when f′(x) is zero?
The next Newton step becomes undefined, so the method stops and a different starting value is needed.
Can the method find every root?
No. The result depends on the function and initial guess, and some equations or guesses do not converge.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
This calculator is intended for educational and numerical-analysis purposes. Results are approximations and should be independently verified for critical scientific, engineering, or professional work.
