How does this calculator work?
The calculator applies the exact closed-form section-property formulas for each profile — the same expressions found in Roark's Formulas for Stress and Strain and standard steel design references — with composite-section first moments used to locate the centroid of asymmetric shapes.
All inputs are converted to a common base unit, the properties are computed from the closed-form expressions shown in the formula reference above, and the results are converted back to your selected unit with the correct dimensional power (lengths scale linearly, areas with the square, section moduli with the cube, and moments of inertia with the fourth power). The diagram redraws live as you type, showing the section to scale with its centroidal axes, so dimension mistakes are caught visually before the numbers are used.
For asymmetric sections — C-channels, T-sections, and L-angles — the centroid is found from first moments of area, and the moment of inertia is transferred to the centroidal axis with the parallel-axis theorem. The optional offset input applies the same theorem in reverse, I' = I + A·d², which is what you need when assembling built-up sections from individual parts.
What each property is used for
| Property | Symbol | Typical use |
|---|---|---|
| Area | A | Axial stress (σ = N/A), weight estimates |
| Centroid | x̄, ȳ | Locating the neutral axis, building composite sections |
| Moment of inertia | Ixx, Iyy | Bending stiffness, deflection (δ ∝ 1/EI), buckling |
| Polar moment | J | Torsional response of circular sections (τ = T·r/J) |
| Elastic section modulus | Sxx, Syy | First-yield bending check (σ = M/S) |
| Plastic section modulus | Zxx, Zyy | Plastic design, ultimate moment capacity (Mp = Z·fy) |
| Radius of gyration | rx, ry | Column slenderness (λ = L/r) for buckling checks |
Note that for non-circular sections, J = Ixx + Iyy is the polar moment about the centroid — it is not the St. Venant torsion constant of open thin-walled sections, which is much smaller. Use dedicated torsion formulas for open-profile torsion checks.
