Calculus & Numerical Methods

Newton-Raphson Root

Find a root of f from an initial guess.

Formula

Formula
xn+1 = xnf(xn)f'(xn)

Variables

SymbolDefinitionType & rangeUnitsRole
f function expression / text x input
x₀ initial guess computed result result

Try it yourself

Interactive calculator
math expression (e.g. x*x, sin(x))
Result

Worked examples

Example 1
Givenf(x) = x*x - 2, guess x₀ = 1
Result1.414213562
Example 2
Givenf(x) = cos(x) - x, guess x₀ = 1
Result0.7390851332