What this calculator does
Everything in structural design comes back to section properties. This calculator derives the area, both second moments of area, the radii of gyration and the section moduli for five standard shapes, which is exactly the data needed for deflection, buckling and stress checks.
How to use it
- Choose the shape, then enter only the dimensions that shape needs — the rest of the inputs are ignored.
- For a rectangle that is width and depth; for a box or channel that is width, depth and wall thickness; for a pipe the diameter and wall; for an I-section the depth, flange width and the two thicknesses.
- Read Iₓ about the strong axis and I_y about the weak axis; the weak axis usually governs stability.
Governing formula
I_x = ∫ y² dA ; r = √(I/A) ; S = I / c Where:
-
A= Cross-sectional area [mm²] -
c= Distance to the extreme fibre [mm]
Derived Equations:
r = √(I/A) S = I/c Z = I/y_max Worked example — 200 × 400 mm solid rectangle
The figures below were produced by running this page's own engine with the example inputs (Shape, Width / flange width (b) (mm), Depth (h) (mm), Wall thickness (mm), Pipe outside diameter (mm), Web thickness (mm), Flange thickness (mm), Flange width (bf) (mm)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Area | 80000 mm² |
|---|---|
| Second moment about the strong axis | 1066666667 mm⁴ |
| Second moment about the weak axis | 266666667 mm⁴ |
| Radius of gyration (strong) | 115.47 mm |
| Radius of gyration (weak) | 57.74 mm |
| Section modulus (strong) | 5333333 mm³ |
| Shape | Rectangle |
- Area = 200 × 400 = 80,000 mm².
- Iₓ = 200 × 400³ / 12 = 1.067 × 10⁹ mm⁴ about the horizontal axis.
- The radii of gyration follow directly: √(I/A) for each axis.
Assumptions & limitations
Engineering calculation. Geometric section properties from first principles: area, second moments of area, radii of gyration and elastic section moduli.
- Geometric properties only — no stress, no strength and no code checks.
- Ignores fillets, root radii and rolled-in radii, which slightly increase the true section properties.
- Holes, slots and cut-outs are not deducted.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- SCI P363 — steel sections: properties and dimensions.
- EN 1993-1-1 Table 5.2 — section properties for standard sections.
- Roark's Formulas for Stress and Strain.