Beam Bending Moment Calculator

About this calculator

For a simply supported beam — resting on two end supports, free to rotate at each — carrying a single point load P at its exact midspan, the maximum bending moment occurs directly under that load and equals M = P·L/4, where L is the span between supports. This comes straight from statics: the reactions at each support are P/2, and the moment builds linearly from zero at each support to its peak at the center.

Structural and civil engineers calculate this moment as one of the first steps in beam design, since it feeds directly into the bending stress check (σ = Mc/I) that determines whether a chosen beam section — timber joist, steel I-beam, or concrete member — is strong enough to carry the load without failing or deflecting excessively.