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Beam Bending Moment Calculator

Enter the central load and span length to get the maximum bending moment.

How it is calculated

The tool uses the textbook result for a simply supported beam with one point load at midspan: Mmax = P × L / 4. P is the load in newtons (N) and L is the span between the two supports in metres (m), so the answer is in newton-metres (N·m). The engine does no unit conversion: a load in kilograms or kilonewtons, or a span in centimetres, gives a number that is wrong by that factor. Zero is accepted and gives 0.00 N·m, but a negative load or length gives no result. Only this one load case is covered, with the load exactly at the centre and the beam's own weight left out.

Worked example

A beam spans 5 m between supports and carries a 12 000 N point load at its centre (about 1.2 tonnes of weight, or 12 kN). Multiply load by span: 12 000 × 5 = 60 000 N·m. Divide by 4: 60 000 / 4 = 15 000. The tool shows a maximum bending moment of 15,000.00 N·m under the load. Each support carries half the load, 6 000 N.

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Common mistakes

  • Entering the load in kilonewtons or kilograms. The field is in newtons, so 12 kN must be typed as 12000, and a mass in kg must first be multiplied by about 9.81 to become a force.
  • Using the beam's total length instead of the span between supports. Overhang past the supports is not part of L in this formula.
  • Applying it to a load that is not at midspan, or to a load spread along the beam. A uniform load gives w·L²/8 instead, and an off-centre point load gives a different value.
  • Forgetting the beam's own weight. It adds its own moment and is not included in this result.
  • Comparing N·m directly with an allowable stress. The moment must still be divided by the section modulus, and the units (N·m versus N·mm) must match before that comparison.

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.

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Comments (1)

  • Editorial team

    Use this figure as a conservative upper bound when the real load is spread out. The same 12,000 N spread evenly over a 5 m span gives a maximum moment of 7,500 N·m, exactly half of the 15,000 N·m shown for a point load at midspan. So treating a distributed load as a midspan point load overestimates the moment by a factor of two. Final member sizes still belong to a structural engineer. What load case are you checking?

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