Round Bar Section Modulus Formula
For a solid round bar, I = πd⁴/64 and S = I/(d/2) = πd³/32. Diameter is powerful: doubling d multiplies section modulus by eight.
Open the section modulus calculatorFormula
For a solid circular section of diameter d:
I = π·d⁴/64
The neutral axis passes through the centre, so c = d/2 and
S = π·d³/32.
Worked example
A 50 mm solid round bar has
I = π × 50⁴ / 64 = 306,796 mm⁴ and
S = π × 50³ / 32 = 12,272 mm³. The same diameter used as a hollow tube
has lower area but can keep much of its bending stiffness if the wall is sized well.
Round bars as beams and shafts
A round bar has the same section modulus in every bending direction, which makes it natural for shafts. For actual shaft deflection and bending stress under a point load, use the shaft deflection calculator.
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.