The centre of mass of a system is the point that represents the average position of the mass distribution. It can be thought of as the weighted average of the position coordinates, where the weighting function is the density of the object.

For a three-dimensional system with a density function , the centre of mass coordinates are given by the weighted average of each coordinate over the region :

Lower Dimensions

For a one-dimensional system along the x-axis, the centre of mass is given by:

For a two-dimensional system in the xy-plane, the centre of mass coordinates are: