Bisection Method Calculator

Bracket a root and halve confidently. See each iteration and stopping rule. Get clean reports for classes and projects.

Calculator Inputs

Allowed: + - * / ^ ( ) and functions like sin(x), sqrt(x), ln(x).
Pick a value where the sign differs from f(b).
The bracket must contain a sign change.
Common values: 1e-3, 1e-6, 1e-10.
Stops early if tolerance is met.
Controls displayed precision (3–16).
Choose how convergence is decided.
Display 10–500 rows (export includes all).
Reset

Iteration Table

Shows a, b, mid, and convergence indicators.
Use Submit to generate an iteration table.

Example Input and Output

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.

Formula Used

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

How to Use This Calculator

  1. Enter f(x) using x as the variable.
  2. Choose bounds a and b so f(a) and f(b) have opposite signs.
  3. Set a tolerance ε and a maximum iteration limit.
  4. Select a stopping rule that matches your requirement.
  5. Press Submit to see the root estimate and iteration table.
  6. Use Download CSV or Download PDF to save results.

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

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.