Bisection Method Calculator

Calculator Inputs

Function f(x)

Allowed: + - * / ^ ( ) and functions like sin(x), sqrt(x), ln(x).

Lower bound (a)

Pick a value where the sign differs from f(b).

Upper bound (b)

The bracket must contain a sign change.

Tolerance (ε)

Common values: 1e-3, 1e-6, 1e-10.

Maximum iterations

Stops early if tolerance is met.

Significant digits

Controls displayed precision (3–16).

Stopping rule

Choose how convergence is decided.

Iteration rows to display

Display 10–500 rows (export includes all).

Reset

Shows a, b, mid, and convergence indicators.

Use Submit to generate an iteration table.

Example	f(x)	a	b	ε	Max iters	Expected root (approx.)
1	`x^3 - x - 2`	1	2	1e-6	50	1.52138
2	`cos(x) - x`	0	1	1e-6	60	0.739085
3	`ln(x) + x - 2`	1	2	1e-6	60	1.557146

Tip: if f(a) and f(b) share a sign, adjust the interval.

Bisection is guaranteed to converge when the function is continuous and the initial interval brackets a sign change.

For best results, bracket tightly and use a small tolerance.