Bisection Method Calculator
Find roots of equations using the bisection (binary search) method.
Function f(x)
Interval [a, b]
Parameters
Bisection Algorithm
- Check f(a) * f(b) less than 0
- Compute midpoint c = (a + b) / 2
- If f(a) * f(c) less than 0, set b = c
- Otherwise, set a = c
- Repeat until |b - a| less than tolerance
Root
1.4142456055
Converged in 14 iterations
f(root)
9.0633e-5
Iterations
14
Iteration History
| n | a | b | c | f(c) |
|---|---|---|---|---|
| 1 | 1.000000 | 2.000000 | 1.500000 | 2.500e-1 |
| 2 | 1.000000 | 1.500000 | 1.250000 | -4.375e-1 |
| 3 | 1.250000 | 1.500000 | 1.375000 | -1.094e-1 |
| 4 | 1.375000 | 1.500000 | 1.437500 | 6.641e-2 |
| 5 | 1.375000 | 1.437500 | 1.406250 | -2.246e-2 |
| 6 | 1.406250 | 1.437500 | 1.421875 | 2.173e-2 |
| 7 | 1.406250 | 1.421875 | 1.414063 | -4.272e-4 |
| 8 | 1.414063 | 1.421875 | 1.417969 | 1.064e-2 |
| 9 | 1.414063 | 1.417969 | 1.416016 | 5.100e-3 |
| 10 | 1.414063 | 1.416016 | 1.415039 | 2.336e-3 |
| 11 | 1.414063 | 1.415039 | 1.414551 | 9.539e-4 |
| 12 | 1.414063 | 1.414551 | 1.414307 | 2.633e-4 |
| 13 | 1.414063 | 1.414307 | 1.414185 | -8.200e-5 |
| 14 | 1.414185 | 1.414307 | 1.414246 | 9.063e-5 |
About Bisection Method
- Always converges if root exists in interval
- Linear convergence rate
- Requires sign change (opposite signs at endpoints)
- Error halves with each iteration
- Simple but slower than Newton-Raphson