Free moment of inertia calculator

How to use the free moment of inertia calculator

This calculator analyses any arbitrary cross section and returns the full set of geometric properties needed for structural design. Build sections from standard shape templates, combine multiple shapes into composite or built-up sections, or enter a fully custom polygon outline.

Section types and input modes

Standard shape templates cover the most common section types: I-sections, T-sections, C-sections (channels), Z-sections, angles, rectangles, hollow rectangles, circles, and hollow circles. Each template requires only the key dimensions - depth, flange width, thicknesses - and fills in the rest automatically.

For non-standard sections, you can combine multiple shapes using the built-up section mode - for example, adding a cover plate to a standard I-section or combining two angles back-to-back. You can also select standard steel sections directly from the built-in database and use them as a starting point.

Analysis modes

The calculator offers four analysis depths. Elastic analysis returns area, centroid, I_x/I_y, elastic section moduli (S_x/S_y), and radii of gyration. Warping and torsion analysis adds J and C_w/I_w. DSM mode adds Direct Strength Method buckling factors for cold-formed steel sections. Full plastic analysis additionally computes plastic section moduli (Z_x/Z_y) and shear areas.

Using properties in design

Copy section properties directly into the free beam analysis calculator to compute deflection and bending moment for any loading. For a standard section not in the library, use the free section properties library. Sign up for a free Calcs.com trial to link your custom sections directly to steel, timber, and concrete design calculators.