Section Properties Calculator

Calculate complete cross-sectional properties for structural steel sections. Get area, moment of inertia, elastic and plastic section modulus, torsion constant, and centroid location for I-beams, channels, angles, and more.

Section Properties Explained

Area (A)

The cross-sectional area in mm² or in². Used to calculate axial stress (σ = P/A) and self-weight. For hollow sections, this is the material area only.

Moment of Inertia (I_yy, I_zz)

The second moment of area about the principal axes, in mm⁴ or in⁴. I_zz is typically the strong axis (resisting bending about the horizontal), while I_yy is the weak axis. These determine bending stiffness and stress distribution.

Torsion Constant (J)

The St. Venant torsion constant in mm⁴ or in⁴. For closed sections (pipes, RHS), J is large and the section resists twisting well. For open sections (I-beams, channels, angles), J is much smaller-these sections are prone to torsional buckling.

Warping Constant (I_w)

The warping constant in mm⁶ or in⁶, quantifies a section's resistance to warping torsion. For open sections (I-beams, channels, tees), warping torsion is the dominant torsional resistance mechanism and I_w is critical for lateral-torsional buckling checks. Closed sections (RHS, CHS) resist torsion primarily through St. Venant torsion and have negligible warping.

Elastic Section Modulus (S_el)

The elastic section modulus in mm³ or in³, calculated as I/c where c is the distance to the extreme fibre. Used to find bending stress: σ = M/S_el. A larger section modulus means lower stress for the same moment.

Plastic Section Modulus (Z_pl)

The plastic section modulus represents the maximum moment a cross-section can carry when fully yielded. It is calculated by finding the plastic neutral axis (PNA) that divides the section into two equal areas, then summing the first moments of those areas. Z_pl is always greater than or equal to S_el, and the ratio Z_pl/S_el is called the shape factor (typically 1.12–1.15 for I-beams, 1.50 for rectangles, 1.70 for circles).

Centroid (C_y, C_z)

The location of the geometric centre of the section. For symmetric sections like I-beams and rectangles, the centroid is at the geometric centre. For asymmetric sections like channels and angles, the centroid shifts toward the heavier portion.

Supported Section Types

Notes on Accuracy

This calculator uses direct closed-form expressions from the entered dimensions. Optional root/corner radii (R) feed into fillet contributions for I-beams, channels, tees and angles, and into the exact rounded-rectangle decomposition for hollow rectangles. Leaving R blank or 0 produces sharp-corner values.

Torsion constant J for open sections is computed from the thin-walled summation (Σbt³/3) with a Trahair fillet correction; this is typically within a few percent of full Saint-Venant FEM values found in manufacturer tables.

For published values that match a standards body or supplier catalogue exactly, consult section tables (AISC, British Steel, ArcelorMittal, etc.) or use our full structural analysis tool which ships with a comprehensive library of standard sections.

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