Second Moment of Area Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Pick the shape you're using and enter its dimensions in millimetres — rectangle (width b, height h), solid circle (diameter d), or tube (outer D, inner d).
- You can fill more than one shape to compare them.
- Read the second moment of area I in mm⁴ (and cm⁴).
How it works
The Second Moment of Area Calculator works out I — the geometric stiffness of a cross-section about its centroidal axis, which drives both bending stress and deflection.
Rectangle: Iₓ = b·h³/12 (and I_y = h·b³/12). Solid circle: I = π·d⁴/64. Tube (hollow circle): I = π·(D⁴ − d⁴)/64. Because depth is cubed, putting material far from the bending axis raises I fast — the reason I-beams and tubes are efficient.
Worked example
100 × 200 mm rectangle. Bending about the strong (horizontal) axis: Iₓ = 100×200³/12 = 66.7×10⁶ mm⁴ = 6667 cm⁴. About the weak axis: I_y = 200×100³/12 = 16.7×10⁶ mm⁴.
Tips
- Make a beam deeper rather than wider — I grows with depth cubed but only linearly with width.
- For the tube, the inner diameter must be smaller than the outer diameter.
Frequently asked questions
What's the difference between Iₓ and I_y?
Iₓ is for bending about the horizontal axis, where the height h resists bending — orient a beam this way (tall) for maximum strength. I_y is about the vertical axis (bending sideways). The tool reports both for rectangles.
Is this the same as the polar moment of area?
No. This is the area moment of inertia for bending. The polar moment (J), used for torsion, is different — for a solid circle J = π·d⁴/32, twice the bending I.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.