Calculate the elastic section modulus (S) for various cross-sectional shapes to determine bending strength.
Last updated: March 2026 | By ForgeCalc Engineering
Section modulus (S) is a geometric property for a given cross-section used in the design of beams or flexural members. It relates the bending moment (M) applied to a beam to the maximum stress (σ) experienced by that beam.
A higher section modulus indicates a stronger cross-section that can resist more bending moment for a given stress level. It is calculated as the ratio of the area moment of inertia (I) to the distance from the neutral axis to the extreme fiber (y).
In engineering, 'S' usually refers to the Elastic Section Modulus (used for elastic design), while 'Z' refers to the Plastic Section Modulus (used for limit state or plastic design).
In the rectangular formula (bh²/6), height is squared. This means doubling the height increases the strength by 4 times, while doubling the width only increases it by 2 times.
The formula is σ = M / S, where σ is the stress, M is the bending moment, and S is the section modulus. This is the fundamental equation for beam design.
You can use any consistent units (mm, cm, inches). The resulting section modulus will be in units cubed (mm³, cm³, in³).
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