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**