Maths & numbers

Polygon centroid calculator

Locate the uniform-area centre of a simple polygon and plot it.

Polygon centroid calculator
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Your inputs

Use exact X,Y headings, without repeating the first point unless closing a polygon.

Up to 25 MB per file, 50,000 data rows, 200 columns and 2 million data cells. Fully blank rows and columns are ignored before row, column and cell limits are checked. Individual tools may have smaller result or chart limits.

Results update as you type. Larger files run when you press Update result.

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A clear answer. Here’s how.

Uses signed shoelace cross-products on translated coordinates to obtain the uniform-area centroid, area and boundary perimeter. Accepts 3–500 ordered vertices and an optional repeated closing point. Rejects duplicate vertices, self-crossing/touching non-adjacent edges and numerically degenerate polygons. This is an area centroid, rather than the arithmetic mean of vertex positions; holes and non-uniform density are unsupported.

See a worked example

Worked example

A fixed demonstration, separate from the values you enter above.

Point CSV
X,Y
0,0
4,0
4,3
0,3

Example result

Centroid X
2
Centroid Y
1.5
Area
12
Perimeter
14

Uniform-area centroid of a simple polygon, not the average of its vertices.

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