Section Properties Calculator
Calculate the cross-section properties of a rectangle, solid circle, hollow circle (tube), isosceles triangle or symmetric wide-flange (I-beam) shape — area, centroid, moment of inertia, section modulus and radius of gyration about both the strong (x-x) and weak (y-y) axes.
Input
mm.
mm.
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/section-properties-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"shape": "rectangle",
"width": "200",
"height": "400"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `section-properties-calculator` tool (Section Properties Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/section-properties-calculator/"
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title="Section Properties Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
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<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
Calculate the area, centroid, moment of inertia, section modulus and radius of gyration of a rectangle, solid circle, hollow circle (tube), isosceles triangle or symmetric wide-flange (I-beam) cross-section — the standard geometric properties an engineer needs before running a bending, deflection or buckling check.
How to use it
- Pick the cross-section shape.
- Enter its dimensions in millimeters — the fields shown adjust to the shape (width/height for a rectangle, diameter for a circle, flange and web dimensions for an I-beam, and so on).
- Read the results: area, centroid location, and the moment of inertia, section modulus and radius of gyration about both the strong (x-x) and weak (y-y) centroidal axes.
Any consistent unit system works — every formula here is dimensionally self-contained, so entering dimensions in inches returns properties in the matching inch-based units.
What each property means
- Area (A) — the cross-sectional area, used for axial stress (σ = P/A) and self-weight calculations.
- Moment of inertia (I) — the second moment of area about a centroidal axis, the key stiffness term in beam deflection (δ ∝ 1/EI) and bending stress.
- Section modulus (S) — I divided by the distance from the centroid to the extreme fiber; bending stress is σ = M/S, so a larger S means lower stress for the same moment.
- Radius of gyration (r) — √(I/A), the effective distance the area is "spread" from the centroid; used in column buckling checks (slenderness ratio = effective length / r).
Shape-specific notes
- Solid circle and hollow circle (tube) are symmetric about every axis through the centroid, so their x-x and y-y properties are identical.
- Isosceles triangle is asymmetric top-to-bottom: the centroid sits at h/3 above the base, not at mid-height, so the section modulus differs between the base fiber and the apex fiber. Both are reported — use the smaller one (the base fiber) for a conservative bending stress check.
- I-beam assumes a symmetric wide-flange shape with identical top and bottom flanges, which is by far the most common rolled/fabricated case. An asymmetric (unequal-flange) section needs a different, non-symmetric formula this calculator doesn't cover.
Limits
These are geometric section properties only — they don't account for material yield strength, buckling mode, or load combinations. Verify results against your governing design code before using them in a structural design.
Privacy
Everything runs in your browser — no dimensions leave your machine.
Related tools
To turn a moment of inertia into an actual deflection, use the Beam Deflection Calculator. For support reactions before checking a beam, use the Beam Reaction Calculator. To check a design against an allowable stress once you have the section modulus, use the Factor of Safety Calculator.