# Centroid

## Mean position of all the points in a shape / From Wikipedia, the free encyclopedia

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In mathematics and physics, the **centroid**, also known as **geometric center** or **center of figure**, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure.^{[further explanation needed]} The same definition extends to any object in $n$-dimensional Euclidean space.^{[1]}

This article includes a list of general references, but it lacks sufficient corresponding inline citations. (April 2013) |

In geometry, one often assumes uniform mass density, in which case the *barycenter* or *center of mass* coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.^{[2]}

In physics, if variations in gravity are considered, then a *center of gravity* can be defined as the weighted mean of all points weighted by their specific weight.

In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center.