Newton's Method Calculator

Find roots of equations using Newton's iterative method

Function f(x) Supported: +, -, *, /, ^, sin(), cos(), tan(), arcsin()/asin(), arccos()/acos(), arctan()/atan(), atan2(), log() or ln() (natural log), log(b, x) (log base b), sqrt(), abs(), exp()

Starting Point (x₀)

Iterations

Animation Speed

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Results

Final Root: -

Final f(x): -

Iterations Used: -

Iteration	x_n	f(x_n)	f'(x_n)

How to Use

Function: Enter the function in terms of x (e.g., x^2 - 4 to find √4)
Starting Point: Choose an initial guess near the root
Iterations: Number of times to apply Newton's method

Basic Operations:

+ (addition), - (subtraction), * (multiplication), / (division)
^ (power/exponentiation), e.g., x^2, 2^x
Implicit multiplication: 2x = 2*x, x(2+3) = x*(2+3)

Trigonometric Functions:

sin(x) - sine
cos(x) - cosine
tan(x) - tangent

Inverse Trigonometric Functions:

arcsin(x) or asin(x) - arcsine (inverse sine), input must be in [-1, 1]
arccos(x) or acos(x) - arccosine (inverse cosine), input must be in [-1, 1]
arctan(x) or atan(x) - arctangent (inverse tangent)
atan2(y, x) - arctangent of y/x (returns angle in correct quadrant)

Logarithmic Functions:

log(x) or ln(x) - natural logarithm (base e)
log(b, x) - logarithm with base b, e.g., log(10, x) for log₁₀(x), log(2, x) for log₂(x)

Other Functions:

sqrt(x) - square root
abs(x) - absolute value
exp(x) - exponential (e^x)

Constants:

pi or PI - π (3.14159...)
e - Euler's number (2.71828...)

Examples:

x^2 - 4 - Find square root of 4
sin(x) - 0.5 - Find where sin(x) = 0.5
log(10, x) - 2 - Find where log₁₀(x) = 2
log(2, x^2) - 3 - Find where log₂(x²) = 3
x^3 - 2*x + 2 - Cubic equation

Newton's Method Formula

x_n+1 = x_n - f(x_n) / f'(x_n)