Bisection method,
drawn out step by step.

Give it an equation and a bracket, and watch the interval close in on the root — one halving at a time, with every approximation and error logged along the way.

Method Bisection (bracketing) Order Linear convergence Needs sign change on [a, b]
Live demo — f(x) = x³ − x − 2step 1

Set up the problem

Sheet 01 / Input

Use x as the variable — powers, trig, logs, roots, and the constants e and pi are all supported.

How do I type my equation?

The parser reads standard math notation. A few examples:

You wantType this
Powersx^3, x^2
Multiplication4*x (or just 4x)
Square rootsqrt(x)
Trig functionssin(x), cos(x), tan(x)
Implicit trigx*tan(x) or shorthand xtan(x)
Exponential eˣexp(x) or e^x
Natural logln(x) or shorthand lnx
Base-10 loglog(x) or log10(x) or shorthand logx
Constantspi, e (Euler's number ≈ 2.71828)
Absolute valueabs(x)
The bounds a and b also accept expressions: type e, pi, 2*pi, sqrt(2), etc. Negative values like -2 are allowed — enter them freely in manual mode.
ln(x) and log(x) are kept separate in this parser: ln(x) is always the natural log, and log(x) is always base-10 (same as log10(x)).
Bracket [a, b]
scans f(x) for a sign change near the curve
type your own bounds below — negative values like −2 are allowed

shown after the decimal point, anywhere from 1 to 8

Stop after…
stops as soon as two consecutive midpoints are identical — the most natural convergence signal
original behaviour — narrows until the bracket width is below 4 × machine epsilon (may take 50 + steps)