The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices 
, ..., 
are
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the polygon area and 
and 
(Bourke 1988, Nürnberg 2013).
Polygon Centroid
See also
Geometric Centroid, Polygon, Polygon AreaExplore with Wolfram|Alpha
References
Bourke, P. "Calculating the Area and Centroid of a Polygon." July 1988. http://paulbourke.net/geometry/polygonmesh/.Nürnberg, R. "Calculating the Area and Centroid of a Polygon in 2D." 2013. https://www.ma.imperial.ac.uk/~rn/centroid.pdf.Cite this as:
Weisstein, Eric W. "Polygon Centroid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolygonCentroid.html