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Polygon Centroid Calculator - Online Center of Mass

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Polygon Centroid Calculator

Find the geometric center (centroid) of any simple polygon – click on the canvas or enter coordinates.

Draw Your Polygon
Click on canvas to add vertices. Mouse shows next segment.
Vertex Coordinates
Format: x,y; x,y
Points 0
#XY
No vertices added.
Results
Centroid: ,
Area:
Perimeter:

Frequently Asked Questions

The centroid is the arithmetic mean position of all points in a polygon. For uniform density, it is the center of mass. It can be thought of as the balancing point if the shape were cut from a sheet of material.

We use the shoelace formula for signed area, then compute the centroid coordinates as weighted averages of vertex coordinates, using edge cross products. This works for any simple polygon (concave or convex).

Not necessarily. For concave polygons, the centroid can fall outside the shape. This calculator gives the mathematical centroid regardless of whether it lies inside.

Yes. The algorithm handles any simple polygon (non-self-intersecting). Irregular shapes and concave polygons are fully supported.

The calculator uses the signed area method, which may still return a value, but the centroid won't correspond to a physical center of mass. For meaningful results, use simple (non-self-intersecting) polygons.

A polygon requires at least three points to enclose an area. With 1 or 2 points, the area is zero, so the centroid is undefined.

You can use any Cartesian coordinate system (x, y). The centroid will be expressed in the same units. All calculations are scale-invariant.

It uses double-precision floating point math. Results are displayed to 4 decimal places, which is accurate enough for engineering and design work.
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