Section Properties — Polygon by Coordinates

1

Geometry

One vertex per line: x, y (counter-clockwise). Further blocks separated by a blank line are treated as holes

The shoelace (Gauss) formulas give the exact area, centroid and second moments of the closed polygon. Curved edges are approximated with a sufficient number of vertices. Vertex order does not matter (the sign is corrected automatically).

2

Geometric properties

Area, centroid, moment of inertia, elastic section modulus, radius of gyration

3

Plastic modulus and torsion

Z_x, Z_y, shape factor, J

4

Principal axes

I_xy, θ, I₁, I₂