Compute area, perimeter, and centroid of any simple polygon with the shoelace (Gauss) formula. Paste coordinates one pair per line — a live preview shows the shape and flags self-intersections.
One vertex per line: x, y or x y. The polygon auto-closes — no need to repeat the first point.
For a polygon with vertices (x₁,y₁), (x₂,y₂), …, (xₙ,yₙ):
A = ½ |Σᵢ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|
The signed area is positive for counter-clockwise winding and negative for clockwise. The centroid is the area-weighted average of triangle fans from the origin.