Try the Second Moment of Area & Section Properties
Calculate area, centroid, second moment of area (Ix, Iy), section modulus, radius of gyration, torsion constant and weight per metre for rectangles.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
What is the Second Moment of Area & Section Properties?
Beam stiffness and strength depend on the cross-section's geometry, not just its area. Select a shape — rectangle, solid round, round tube, rectangular tube, I/H-beam, T-section, channel or angle — enter its dimensions in millimetres and the calculator returns the area, the centroid, the second moments of area Ix and Iy about the centroidal axes, the elastic section moduli, the radii of gyration, an approximate torsion constant J, the extreme-fibre distances and the weight per metre for the density you choose.
Composite shapes are computed with the parallel-axis theorem from their constituent rectangles, and circular shapes with the exact closed-form formulas. A section drawing shows the shape and its centroid. Use the results directly in the beam deflection calculator or any bending-stress calculation.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Rectangle, round bar, tube, rectangular tube, I-beam, T, channel, angle.
A, centroid, Ix, Iy, Sx, Sy, rx, ry, J and weight per metre.
Closed-form for circles; parallel-axis composition for the rest.
Section sketch with the centroid marked.
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It opens in your browser, so there is nothing to download.
Used for
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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 second moment of area?
A geometric property (mm⁴) that measures how a cross-section resists bending: I = ∫y² dA.
How is section modulus defined?
S = I ÷ c where c is the distance from the neutral axis to the outer fibre.
Are fillets included?
No — sharp corners are assumed, so values are slightly below catalogue figures.
Can I enter inches?
Use mm; convert inches by multiplying by 25.4.
How do I use the Second Moment of Area & Section Properties?
1. Choose the shape. 2. Enter its dimensions in mm. 3. Read the properties and the extreme-fibre distances. 4. Use I and c in your bending or deflection calculation.
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Try the Second Moment of Area & Section Properties now
Area, centroid, Ix, Iy, section modulus, radius of gyration for common sections. Free to use.
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