Section Modulus Calculator

About this calculator

When a beam bends, the bending stress it experiences at the outer fiber follows σ = M/S, where M is the applied bending moment and S is the cross-section's elastic section modulus — a purely geometric property that tells you how efficiently a shape resists bending regardless of material. For a solid rectangular cross-section of width b and height h, S = b·h²/6, derived from the moment of inertia I = b·h³/12 divided by the distance c = h/2 from the neutral axis to the extreme fiber.

Structural engineers use section modulus, alongside allowable stress values from codes like AISC (steel) or Eurocode, to size joists, beams and lintels so bending stress under design loads stays safely below the material's yield strength — it's one of the first checks in any beam-sizing calculation, whether for a timber floor joist or a steel I-beam.