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Bisection Method Step Calculator

One bisection step on the bracket [a, b].

Perform one bisection-method step: compute the midpoint m of the bracket [a, b], evaluate the new bracket based on the sign of f(a)·f(m), and report the half-interval as an error bound.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

m = (a + b) / 2. If f(a)·f(m) < 0, the next bracket is [a, m]; otherwise it is [m, b]. Error bound = (b − a) / 2.

In depth

Perform one bisection-method step: compute the midpoint m of the bracket [a, b], evaluate the new bracket based on the sign of f(a)·f(m), and report the half-interval as an error bound.