Definition. Let m1, m2, ..., mr be masses which are located at the points x1, x2, ..., xr on the x-axis.

The moments of the masses with respect to the x-axis is

The center of mass of the system is

where

is the sum of the masses.
Definition. Let m1, m2, ..., mr be masses which are located at the points (x1, y1), (x2, y2), ..., (xr, yr) on the plane.

The moments of the masses with respect to the y-axis is

The moments of the masses with respect to the x-axis is

The center of mass of the system is

where

is the sum of the masses.

Definition. Let T be a flat plate with uniform density r which is defined as the area between two continuous functions y = f(x) and y = g(x) with f(x) > g(x) for all x in [a, b].

The moment of T with respect to the y-axis is

The moment of T with respect to the x-axis is

The center of mass of the system is

where

is the mass of T.