Your Composite Section Moment of Inertia Calculator
Calculate the area, centroid, moments of inertia (Ix, Iy, Ixy), principal axes, section moduli and radii of gyration of a composite cross-section built.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
Sample input: Width = 100; Height = 20; x = 0; y = 90. Pressed Add shape.
What is the Composite Section Moment of Inertia Calculator?
Real cross-sections are rarely a single standard shape. This calculator lets you build one from simple pieces — rectangles, circles, ellipses, isosceles and right triangles and semicircles, any of which can be a hole — place each piece by the coordinates of its bounding-box centre, rotate it in 90° steps, and get the properties of the whole section: area, centroid, centroidal moments of inertia Ix and Iy, the product of inertia, the polar moment, principal moments and angle, section moduli at the extreme fibres and radii of gyration. A live drawing shows the shapes, holes in dashed red, and the centroid with its axes.
Each piece's own centroidal inertia is transferred to the combined centroid with the parallel-axis theorem and holes are subtracted. Examples load a T-section, an I-beam, a round tube, a rectangle with a semicircular cap and an L-section with a hole. Results were verified against closed-form solutions: circle πd⁴/64, semicircle (π/8 − 8/9π)r⁴ about its centroid and a T-section by parallel axis.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Rectangle, circle, ellipse, triangles, semicircle — add holes by ticking Hole.
A, centroid, Ix, Iy, Ixy, J, principal axes, S and r.
See your section with the centroid and axes.
T, I, tube, rectangle with cap, L with hole.
AZRS tools are free to open and use.
It opens in your browser, so there is nothing to download.
Used for
Pick one to see how it fits.
How it compares
A plain look at this tool next to the usual alternative.
| This engineering calculator | Desktop software | |
|---|---|---|
| Install | Nothing to install | Usually an app or program to install |
| Account | No signup | Depends on the product |
| Cost | Free to use | Free or paid, depends on the product |
| Where it runs | In your browser tab | On your computer |
Questions people ask
What is Ixy?
The product of inertia; zero for sections symmetric about an axis.
Can I draw any shape?
Any combination of the supported primitives, with holes.
What are principal axes?
The orientation where Ixy = 0 and inertia is maximum/minimum.
Is it free?
Yes.
How do I use the Composite Section Moment of Inertia Calculator?
1. Add shapes and enter their size and bounding-box centre. 2. Tick Hole for cut-outs and rotate as needed. 3. Read the section properties. 4. Compare with the drawing to check the layout.
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Centroid, moment of inertia and section modulus of any shape built from rectangles. Free to use.
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