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Section Modulus Calculator

Calculate Elastic Section Modulus (S or Z) for beams. Compare the strength-to-weight ratio of different shapes.

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Category Engineering Calculators

Section 1

Sx: -
Area: -
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About

The Elastic Section Modulus (S) is the primary geometric property used to calculate bending stress in beams under load. Engineers use it to select the most efficient beam profile that keeps stress below the material's yield limit. A higher Section Modulus implies greater resistance to bending for a given cross-sectional area.

This tool calculates Sx and Sy for common shapes. It includes a unique "Comparison Mode" allowing engineers to test two different geometries side-by-side (e.g., a deep rectangular beam vs. a square beam of equal area) to determine which offers superior structural performance.

beam design stress analysis section modulus bending moment

Formulas

The Section Modulus is derived from the Moment of Inertia (I) and the distance to the extreme fiber (c or y):

S = Ic

Stress (σ) is calculated as:

σ = MS

Reference Data

ShapeFormula (S)Notes
Rectanglebh26Doubling height quadruples strength.
CircleπD332Symmetric in all axes.
Hollow BoxBH3 − bh36HEfficient strength-to-weight.

Frequently Asked Questions

Elastic Modulus (S) assumes the material behaves linearly and fails at the first yield point. Plastic Modulus (Z) assumes the entire section has yielded (plastic hinge), used in ultimate strength design. This tool calculates S.
It allows for a direct link between the external load (Moment) and internal material capacity (Yield Stress). It simplifies beam selection to checking if S_required < S_provided.