Bisection Method Calculator
Bracket a root and halve the interval, safely every time.
Enter your values
ⓘ Live results
Results
- Midpoint c
- 1.5
- Current error bound
- 0.5
- Steps to reach target accuracy
- 14
- Next bracket if f(c) shares the sign of f(a)
- [1.5, 2]
- Next bracket if f(c) shares the sign of f(b)
- [1, 1.5]
- Bracket valid?
- Yes — the signs differ, so a root lies inside
Quick answer
Bisection repeatedly halves an interval where the function changes sign, guaranteeing convergence with the error halving every iteration.
error after n steps = (b − a) ÷ 2ⁿ
How to use the Bisection Method Calculator
- 1Find two x values where the function has opposite signs.
- 2Enter the interval and those two function values.
- 3Take the midpoint, evaluate the function there and repeat with the half that still changes sign.
Worked example
Using the values the calculator loads with:
Inputs
- Interval start a1
- Interval end b2
- f(a)-1
- f(b)5
- Target accuracy0.0001
Results
- Midpoint c1.5
- Current error bound0.5
- Steps to reach target accuracy14
- Next bracket if f(c) shares the sign of f(a)[1.5, 2]
- Next bracket if f(c) shares the sign of f(b)[1, 1.5]
- Bracket valid?Yes — the signs differ, so a root lies inside
Frequently asked questions
Why use bisection when Newton is faster?
Because bisection cannot fail once you have a bracket. It is the reliable fallback when Newton diverges.
How accurate is it after 20 steps?
The interval shrinks by a factor of about a million, so a starting width of 1 becomes roughly 0.000001.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.