Rectangular Section Modulus Formula
For a solid rectangular section bending about its horizontal centroidal axis, I = b·h³/12 and S = I/c = b·h²/6. Depth matters most because I grows with h cubed.
Open the section modulus calculatorFormula
For a rectangle of width b and height h:
I = b·h³/12
The neutral axis is at mid-depth, so c = h/2 and
S = I/c = b·h²/6.
Worked example
A 50 × 100 mm rectangle has
I = 50 × 100³ / 12 = 4,166,667 mm⁴ and
S = 50 × 100² / 6 = 83,333 mm³. Doubling the height to 200 mm would
multiply I by eight and S by four.
Use in bending stress
Once section modulus is known, peak elastic bending stress is
σ = M / S. The same material and bending moment will see lower stress
when S is larger, which is why beams are usually deep rather than wide.
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.