In

mathematics and

physics, the

**centroid** or geometric center of a two-dimensional region is, informally, the point at which a cardboard cut-out of the region could be perfectly balanced on the tip of a pencil (assuming uniform

density and a uniform gravitational field). Formally, the

**centroid** of a plane figure or two-dimensional shape is the arithmetic mean ("average") position of all the points in the shape. The definition extends to any object in n-dimensional space: its

**centroid** is the mean position of all the points in all of the coordinate directions.

While in

geometry the term

barycenter is a synonym for "

**centroid**", in

physics "

barycenter" may also mean the physical

center of mass or the

center of gravity, depending on the context. The

center of mass (and

center of gravity in a uniform gravitational field) is the arithmetic mean of all points weighted by the local

density or

specific weight. If a physical object has uniform

density, then its

center of mass is the same as the

**centroid** of its shape.

Centroid, Wikipedia
See Also

**Balance**
**Barycenter**
**Center**
**Center of Gravity**
**Center of Mass**
**Neutral Center**