Centroid Of A Polygon Calculator

Work out centroid of a polygon instantly with clear inputs, formula shown and shareable results.

About Centroid Of A Polygon Calculator

The area centroid of a polygon weights each edge's cross product by the midpoint of that edge: Cx = (1/6A)Σ(xₖ + xₖ₊₁)(xₖyₖ₊₁ − xₖ₊₁yₖ), and similarly for Cy. This is not the same as the plain average of the vertices unless the polygon is regular.

Formula

Polygon centroid

Cx = (1/6A)Σ(xₖ+xₖ₊₁)·crossₖ, Cy = (1/6A)Σ(yₖ+yₖ₊₁)·crossₖ, A = ½Σcrossₖ

Worked example

With the default values below, Centroid Of A Polygon Calculator returns Centroid of (3, 2). Change any input above and every figure here is recalculated in your browser.

Inputs used

Vertices in order (x, y pairs): 0,0 6,0 6,4 0,4
Real-world units per coordinate unitminimum 0: 1

Results

Centroid: (3, 2)
Centroid x: 3.0000
Centroid y: 2.0000
Polygon area: 24.0000

Step by step

1Values used
2Polygon centroid
3Centroid= (3, 2)
4Centroid x= 3.0000
5Centroid y= 2.0000
6Polygon area= 24.0000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Rectangle 0,0 6,0 6,4 0,4?

The centroid is (3, 2), the middle of the rectangle, with area 24.

Why not just average the vertices?

Vertex averaging weights corners equally and gives the wrong answer whenever the edges have unequal lengths.