How this calculator works
A cross-sectional area is the area you see when a solid is cut by a plane. For a solid shape it is the outline area, and for a hollow or open section the empty part is subtracted. This calculator builds each section from rectangles, triangles and circles, so the answers assume sharp corners and uniform wall thickness. Real rolled or extruded sections have rounded fillets and tapered flanges, which make their published areas slightly different from these idealised figures.
Formula
Rectangle: WH. Hollow rectangle: WH - (W - 2t)(H - 2t). I section: 2Wt_f + (H - 2t_f)t_w. C section: Ht_w + 2(W - t_w)t_f. T section: Wt_f + (H - t_f)t_w. L section: t(W + H - t). Isosceles triangle: ½BH. Equilateral triangle: (√3/4)L². Circle: πD²/4. Tube: πt(D - t).
Worked example
A rectangle 10 mm wide and 20 mm high has area 200 mm². A tube with outside diameter 10 mm and wall thickness 1 mm has area π × 1 × (10 - 1) = 9π ≈ 28.2743 mm². An I section with flange width 10 mm, height 20 mm, web 1 mm and flanges 2 mm has area 2 × 10 × 2 + 16 × 1 = 56 mm².
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Frequently asked questions
What do the web and flange thicknesses mean?
The web is the vertical plate joining the flanges. Each flange is a horizontal plate at the top or bottom. The I section has two flanges, the C and T sections one each, and the L section has no separate flange.
Why is the result different from a steel table?
Published section properties use the rounded fillets and root radii of the real profile. This calculator treats every section as sharp-cornered rectangles, so it gives the idealised area.
Does the orientation of an I section matter?
Not for area. Bending stiffness depends on how far material sits from the neutral axis, which is why the moment of inertia calculator is the better tool for structural work.
Can I use inches?
Yes. Each dimension is converted to metres before the formula runs, and the result can be shown in square metres, square feet or square inches.