Section Properties Calculator (Second Moment of Area and Section Modulus)
Area, second moment of area (moment of inertia), section modulus and radius of gyration for rectangles, solid and hollow round bars, rectangular hollow sections, I-beams, T-sections and channels. Every property is taken about the centroidal axis, so Ix and Wx match the values printed in steel section tables, and T-sections and channels also report the centroid position and both extreme-fibre moduli.
How to use this calculator
- Pick the cross section shape.
- Enter the dimensions in millimetres; the fields that do not apply to the chosen shape are ignored.
- Read the area, centroid position, Ix and Iy, the section moduli and the radii of gyration.
Frequently asked questions
What is the difference between the second moment of area and the moment of inertia?
The second moment of area I, in mm4, is a pure geometric property of the cross section and is the quantity that the bending stress and deflection formulas use. The mass moment of inertia, in kg mm2, depends on density and describes resistance to angular acceleration. This calculator reports the geometric second moment of area.
Why does a T-section have two different section moduli?
For a symmetric section the centroid sits at mid depth and Wx = Ix / (h/2) is a single number. For a T-section or channel the centroid is off centre, so the top and bottom fibres sit at different distances from the neutral axis and each has its own modulus. Bending stress M / W must be checked on both fibres, and the shortest side carries the higher stress.
Do these values match the properties printed in steel section tables?
They match for the idealised sharp-cornered geometry entered here. Published tables for rolled sections include root radii, flange taper and web-to-flange fillets, so a real rolled I-beam is a few percent stiffer than the rectangle approximation. For final design use the manufacturer's tabulated Ix, and use this calculator for built-up welded sections where no table exists.