Tube Section Modulus Formula

Tube section modulus is found by subtracting the hollow core from the outside shape. For round tube, I = π(OD⁴ - ID⁴)/64 and S = I/(OD/2).

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Round tube formula

For a round tube with outside diameter OD, wall thickness t and inside diameter ID = OD - 2t: I = π·(OD⁴ - ID⁴)/64 The extreme fibre distance is c = OD/2, so S = I/c.

Rectangular tube formula

For rectangular tube with outside width b, outside height h and wall t, subtract the inner rectangle: I = [b·h³ - (b-2t)(h-2t)³] / 12, then S = I / (h/2).

Worked example

A 50 mm OD × 5 mm wall round tube has ID = 40 mm. I = π(50⁴ - 40⁴)/64 = 181,132 mm⁴ and S = 181,132 / 25 = 7,245 mm³. It is much lighter than a solid 50 mm bar while keeping a useful fraction of the bending stiffness.

Related structural tools

Section modulus calculator for rectangle, round, tube, I-beam, channel, tee and angle.
Shaft deflection calculator for round shafts used as beams.
Square tube deflection calculator for HSS-style beam checks.

Last reviewed: June 1, 2026.