TOOLS / STRUCTURAL

Section properties calculator

Get area, second moment of area, elastic and plastic section moduli and radius of gyration for rectangles, circles and hollow sections — the geometry a beam check starts from.

Cross-sectional area A20000 mm²

Ix: 66666667 mm⁴ · Iy: 16666667 mm⁴ · Sx: 666667 mm³ · Sy: 333333 mm³ · Zx: 1000000 mm³ · Zy: 500000 mm³ · rx: 57.74 mm · ry: 28.87 mm.

Geometry only: A (area), I (second moment of area), S (elastic section modulus, I/c), Z (plastic section modulus) and r (radius of gyration, √(I/A)). This tool does not check strength, buckling or deflection — use its outputs as inputs to a proper structural check by a qualified person where loads are involved. Unlike the metal-weight tool, which outputs weight only, this tool outputs I, S, Z and r.

Formula

Rectangle: A = b·h, Ix = b·h³ ÷ 12, Sx = Ix ÷ (h/2), Zx = b·h² ÷ 4, rx = √(Ix ÷ A). Circle: I = π·d⁴ ÷ 64, S = I ÷ (d/2), Z = d³ ÷ 6, r = d ÷ 4. Hollow sections subtract the inner shape on the same formulas. The y-axis values swap width and depth.

Standard / source

Standard mechanics-of-materials section formulas, consistent with steel section tables (for example AISC Manual section properties). Published steel tables remain the reference for rolled sections with fillets and corner radii, which this idealised geometry does not model.

Worked example

Rectangle 100 mm wide × 200 mm deep: A = 100 × 200 = 20,000 mm²; Ix = 100 × 200³ ÷ 12 = 66,666,667 mm⁴; Sx = 66,666,667 ÷ 100 = 666,667 mm³; Zx = 100 × 200² ÷ 4 = 1,000,000 mm³; rx = √(66,666,667 ÷ 20,000) = 57.74 mm. These are the calculator's default inputs, so it shows A = 20,000 mm² on load.

Safety note

Geometry only. This tool does not check strength, buckling or deflection — feed its outputs into a proper structural check by a qualified person where loads are involved. Note the distinction from the existing metal-weight tool: that tool outputs weight only, not I, S, Z or r, which is why this is a separate page.