Bissecção (1 passo)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
bissecção
About this calculator
The bisection calculator performs a single step of the bisection method to find roots of functions. Given an interval [a, b] that contains a root, it calculates the midpoint m = (a + b) / 2 and evaluates the function at that point. The method is used to approximate solutions of nonlinear equations when the function is continuous and changes sign in the interval.
It works based on the intermediate value theorem. If f(a) and f(b) have opposite signs, there is at least one root between a and b. The calculator returns the midpoint and f(m), allowing the user to decide the next interval: if f(a) and f(m) have opposite signs, the root is in [a, m]; otherwise, in [m, b]. This is the first step of an iterative process.
Use this calculator in engineering, physics, or mathematics problems where you need to numerically find a root of an equation, such as calculating equilibrium points, zeros of polynomials, or solutions of differential equations. It is useful to start a full bisection process by quickly checking the midpoint.
Caution: the bisection method converges slowly but is guaranteed. Ensure that f(a) and f(b) have opposite signs. If not, the method does not apply. Also, the result is only an approximation; for higher precision, repeat the process with the new interval.
Frequently asked questions
What if f(a) and f(b) have the same sign?
The bisection method does not apply. You need to choose a new interval [a, b] where the function changes sign.
How many iterations are needed for good accuracy?
It depends on the initial interval and desired precision. Each iteration halves the error; for example, 10 iterations reduce the error by a factor of 1024.
Can I use it for discontinuous functions?
No, the method requires the function to be continuous on the interval to guarantee the existence of a root.
What does the returned f(m) value mean?
f(m) is the function value at the midpoint. If it is close to zero, m is near the root. The sign of f(m) indicates which subinterval contains the root.
Does this calculator solve the equation completely?
No, it only provides the first step. To get the root accurately, you must repeat the process manually or use a calculator that iterates automatically.