Polygon Centroid Calculator

About this calculator

The centroid of a simple polygon is its geometric center of mass, the average position of all the points inside its boundary assuming uniform density, and it is not generally the same point as the average of its vertex coordinates except for special shapes like regular polygons. This calculator finds it using the shoelace formula approach: the polygon's signed area and centroid coordinates are computed from a sum over consecutive vertex pairs, weighting each edge's contribution by the cross product of its endpoint coordinates.

CAD and GIS software use this exact method internally whenever a user draws an irregular polygon and asks for its center point, structural and mechanical engineers use it to locate the center of mass of a cross-section for load and stress calculations, and computer graphics engines use it for placing labels or pivot points on arbitrary polygon shapes.

Enter the coordinates of each vertex of your polygon in order and this calculator returns the exact centroid coordinates.