Irregular Polygon Area Calculator

Compute polygon area with the shoelace formula from ordered vertex coordinates.

Last updated: June 2026 | By Patchworkr Team

Vertex List

Coordinates (x,y), one pair per line

Math check: area = 1/2 |sum(x_i y_next - x_next y_i)|

Result

Enter ordered vertices to compute area and perimeter.

Formula

area = 1/2 |sum(x_i y_next - x_next y_i)|

For the rectangle (0,0), (4,0), (4,3), (0,3), the area is 12 and the perimeter is 14.

The shoelace sum gives the same area as the usual rectangle formula.

The vertices must describe a simple polygon and be entered in traversal order for the shoelace formula to be valid.

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