Analysis & loading · Sections & mechanics

Section properties: arbitrary polygon calculator

Area, centroid, second moments, product of inertia, principal axes and section moduli for any polygon given by its vertices.

Standard: Shoelace / Green's theorem · principal axes

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Input	Value	Unit
Vertices x, y (mm), in order	0, 0 400, 0 400, 60 230, 60 230, 540 400, 540 400, 600 0, 600 0, 540 170, 540 170, 60 0, 60

Mohr circle explorer — Principal stresses, maximum shear and the stresses on any plane. Change θ and watch the point move around…
Euler buckling (end conditions) — Critical buckling load and stress for the four classic end conditions.
Torsion of thin-walled closed sections (Bredt) — Shear flow q = T/(2Ao), wall shear stresses and torsion constant J = 4Ao²/∮ds/t for a rectangular box.
Strain rosette (0/45/90) — Principal strains, direction and principal stresses (plane stress) from a 0°/45°/90° rosette.
Thick-walled cylinder (Lamé) — Hoop and radial stresses at the bore and outside surface under internal and external pressure, with von…
Continuous beam (stiffness method) — Any number of spans with UDLs; exact BMD, SFD, reactions and deflected shape. End fixity selectable.

For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.