Bisection method is used for finding root of the function in given interval.


Function f, which is continous function and interval [a,b]. Function must satisfy given equation: f(a) * f(b) < 0 - signs of that values are different, which means that given function in given interval has at least one root in interval [a,b].
Root in given interval.
1. Calculate c - midpoint of given interval using formula: c = (a + b) / 2.
2. Calculate f(c).
3. If b - a is small enough or abs(f(c)) is small enough: return c - which is the root we were searching for;
4. If(f(a) * f(c) < 0) assign c to b, else assign c to a.
5. Go to step 1.

Step By Step:

  • Bisection Method Step 1
    Bisection Method Step 1

Sample Output:

f(x) = x * (x * (x * (x * (x)) + 2)) - 2

root: 0.8515625

Bisection Method Step By Step

Iteration Numberacbf(cn)
70.843750.8593750.875 0.022470533847808838
80.843750.85156250.859375 -0.023827489465475082


  • easy to implement.
  • no need to calculate derivative of given function.


  • slow compared to other methods.
Python Implementation C++ Implementation C# Implementation Java Implementation Matlab Implementation R Implementation

Bisection Method Algorithm
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