📏 Section Properties

Area, second moment of area, section modulus, radius of gyration and weight per metre for the most common cross-sections – and one click to use the result in the Beam Calculator.

Cross-section

Material

Results

→ Use I and E in the Beam Calculator

Formulas

Section	Area A	Second moment of area I (strong axis)
Rectangle b × h	b·h	b·h³ / 12
Round bar, diameter d	π·d² / 4	π·d⁴ / 64
Round tube D × t	π·(D² − d²) / 4	π·(D⁴ − d⁴) / 64, with d = D − 2t
Rectangular tube B × H × t	B·H − (B−2t)·(H−2t)	[B·H³ − (B−2t)·(H−2t)³] / 12
I-beam h × b, web t_w, flange t_f	2·b·t_f + (h−2t_f)·t_w	[b·h³ − (b−t_w)·(h−2t_f)³] / 12

The elastic section modulus is W = I / z_max (the distance from the centre to the outer fibre), and the radius of gyration is i = √(I / A). The bending stress is then σ = M / W.

Real profiles differ by a few percent because of rounded corners and fillets. Rolled I-beams have fillets between web and flange, so the table values are higher: for an IPE 300 (h = 300, b = 150, t_w = 7.1, t_f = 10.7 mm) this tool gives about 8000 cm⁴, the steel table 8356 cm⁴. Hollow sections have rounded corners, so the table values are lower. Use the manufacturer's tables for real profiles.

For learning and quick checks only. Real structures must be designed by a licensed engineer according to the valid standards.