I-Beam Section Modulus Formula

For a simplified sharp-corner I-beam or wide-flange section about its strong axis, subtract the web-height void from the outer rectangle, then divide I by half the depth.

Open the section modulus calculator

Formula

For overall depth d, flange width bf, flange thickness tf and web thickness tw: I = [bf·d³ - (bf - tw)(d - 2tf)³] / 12 The strong-axis neutral axis is at mid-depth, so S = I / (d/2).

Worked example

For a sharp-corner 200 mm deep section with 100 mm flanges, 10 mm flanges and a 6 mm web, the calculator gives I ≈ 16.8 × 10⁶ mm⁴ and S ≈ 168,000 mm³. Published rolled-shape tables may be higher because real root fillets add area near the web/flange junction.

Use catalogue values for real rolled beams

This formula is for idealized geometry and quick comparisons. For a specified W, UB, UC or IPE shape, use the mill catalogue section properties for final design, including root radii, taper and rolling tolerances.

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.