Water Resources HubFree calculator
Composite Centroid & Moment of Inertia
Build any cross-section from rectangles, right triangles, and circles — including cut-out holes — and the calculator returns the composite centroid and the second moments of area about the centroidal axes, using the parallel-axis theorem.
x̄ = Σx̃iAi / ΣAi ŷ = ΣŷiAi / ΣAi
Ixx = Σ(Īxx,i + Aidy,i²) Iyy = Σ(Īyy,i + Aidx,i²)
| x̃i, ŷi | centroid of shape i (rectangle/triangle: from its reference corner; circle: its centre) |
| Īxx,i, Īyy,i | shape i's own centroidal second moments (rectangle bh³/12, right triangle bh³/36, circle πr⁴/4) |
| dx,i, dy,i | distance from shape i's centroid to the composite centroid — the parallel-axis shift |
| Holes | ticked as “hole” — their area is subtracted from the total |
For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.