Moment of inertia calculator for an arbitrary cross-section
Draw the outline of the section — the moments of inertia Ix and Iy, the polar moment, the area, the centroid and the section moduli are computed in your browser as you draw.
Interactive canvas: draw the outline of the cross-section with the mouse, by touch or by entering coordinates. The moments of inertia are recomputed automatically.
Loading the geometry engine…
Press and drag to draw a rectangle
About the calculator
Shape Moment computes the geometric properties of a plane cross-section: the moments of inertia Ix and Iy, the polar moment Ip, the area A, the coordinates of the centroid and the section moduli Wx and Wy. Standard shapes — rectangle, circle, triangle — and arbitrary polygons with holes are all supported.
The outline is triangulated by a WebAssembly build of the Triangle library, and the moments are integrated exactly over the resulting triangles. Several shapes are combined into one section through the parallel-axis theorem, so a composite profile can be assembled from parts.
Everything runs locally in the browser: no registration, no upload, no server round-trip. The tool is aimed at students of strength of materials, structural and mechanical engineers, and anyone who needs a quick check of a section.
What it computes
- Moments of inertia Ix, Iy
- Second moments of area about the centroidal axes or about any point you choose.
- Polar moment Ip
- The sum Ix + Iy, used in torsion calculations.
- Area and centroid
- Exact area of a section with holes and the coordinates of its centre of gravity.
- Section moduli Wx, Wy
- Ratio of the moment of inertia to the distance to the extreme fibre.
- Radii of gyration
- ix and iy, needed for buckling checks.
- Arbitrary geometry
- Polygons with any number of vertices and any number of internal holes.