Section Properties Calculator

Calculate geometric properties for common solid, hollow, I, channel, tee, and angle sections: area, centroid, second moments of area, section moduli, and torsion properties where implemented.

• Need a freeform, built-up, curved, or holed section? Use the Custom Section Builder.
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• Analyse library sections and saved custom sections in Structural FEA for deflections, internal forces and stresses.

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 reported axes, in mm⁴ or in⁴. The strong axis is whichever reported axis has the larger value; the weak axis has the smaller value. For common deep sections this is usually I_zz, but flat or wide sections can have the opposite ordering.

Torsion Constant (J)

The Saint-Venant torsion constant in mm⁴ or in⁴. Closed thin-walled sections generally have much larger J than comparable open sections. Open-section torsion may also require warping and member-stability checks; J alone does not describe buckling resistance.

Warping Constant (I_w)

The warping constant in mm⁶ or in⁶ is one property used in nonuniform-torsion and lateral-torsional-buckling formulations. This calculator displays I_w only for I, channel, and tee sections where it is implemented. Whether warping is important depends on member length, restraint, section, and loading; a zero or omitted page result must not be read as a universal physical statement.

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)

For a homogeneous section with uniform yield stress, Z_pl is the geometric term in the ideal fully plastic moment M_pl = f_yZ_pl; design resistance still depends on the governing code. 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 greater than or equal to S_el, and Z_pl/S_el is the shape factor (about 1.12–1.15 for many I-sections, 1.50 for rectangles, and 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. For I-beams, channels, tees and angles the optional radius R is the root fillet at the web-flange junction. For hollow rectangles it is the outside corner radius r_o, and the inside radius is taken as r_o − t in an exact rounded-rectangle decomposition. Cold-formed tube typically has r_o of 2t to 2.5t (AS/NZS 1163 uses 2.5t above 3 mm wall). Many tables list the inside radius instead, so add t before entering it. Leaving R blank or 0 produces sharp-corner values. Real cold-formed sections always have rounded corners, so sharp-corner I and S overstate the catalogue values: an RHS 150×50×6 gives about 13% more Ix with sharp corners than with r_o = 15 mm, and about 7% more if its 9 mm inside radius is entered as r_o.

Torsion constant J for open sections is computed from a thin-wall summation (Σbt³/3) with the project's fillet correction. Treat it as a geometric approximation and compare it with a supplier catalogue or validated section analysis when torsion affects design.

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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