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Calculator · Structural · Composite section · Parallel-axis theorem

Centre of inertia (composite section)

Add rectangles, circles, and holes to build up any cross-section. Get the composite centroid (x̄, ȳ) plus Ix and Iy about the overall centroidal axes — computed automatically through the parallel-axis theorem. Reviewed by a licensed PE.

COMPOSITE SECTION · CENTROID + PARALLEL-AXIS x y A₁ = 280×240 (x₁, y₁) A₂ − A₃ − A₄ − (x̄, ȳ) x̄ ȳ PARALLEL-AXIS THEOREM I = Iᶜ + A·d² Iᶜ — sub-shape centroidal I A — sub-shape area (signed) d — sub-shape→composite dist CENTROID x̄ = Σ(Aᵢ·xᵢ) / Σ Aᵢ ȳ = Σ(Aᵢ·yᵢ) / Σ Aᵢ COMPOSITE I Iₓ = Σ(Iₓ,ᵢ + Aᵢ·dᵧ²) Iᵧ = Σ(Iᵧ,ᵢ + Aᵢ·dₓ²)
Figure 1 — Built-up section: main rectangle with two rectangular cut-outs and one circular hole; centroid (x̄, ȳ) and parallel-axis theorem.

Use the composite centroid calculator

Add sub-shapes one by one — each row is a rectangle (b × h) or circle (D) at coordinates (xc, yc). Tick "hole" to subtract i