Bisection Method Calculator
Bracket a root and halve the interval, safely every time.
Enter your values
Enter the interval start a you are working with.
Enter the interval end b you are working with.
Enter the f(a) you are working with.
Enter the f(b) you are working with.
Enter the target accuracy you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Bracket a root and halve the interval, safely every time. |
|---|---|
| Category | Math |
| Inputs needed | Interval start a, Interval end b, f(a), f(b), Target accuracy |
| Main output | Midpoint c |
| Formula | error after n steps = (b − a) ÷ 2ⁿ |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Interval start a
- Enter the interval start a you are working with.
- Interval end b
- Enter the interval end b you are working with.
- f(a)
- Enter the f(a) you are working with.
- f(b)
- Enter the f(b) you are working with.
- Target accuracy
- Enter the target accuracy you are working with.
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.
What do I need to enter into the Bisection Method Calculator?
Just 5 values: interval start a, interval end b, f(a), f(b), target accuracy. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Bisection Method Calculator work out the answer?
Bisection repeatedly halves an interval where the function changes sign, guaranteeing convergence with the error halving every iteration. It applies the formula error after n steps = (b − a) ÷ 2ⁿ and shows the working so you can check each step by hand.
Is the Bisection Method Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.