In the previous section, Centroid: Line, Area and Volume , it was shown that the centroid of an object involves evaluating integrals of the form

where Q is a line, area, or volume, depending on the centroid that is required. The same equation can also be used for the other two directions by just substituting y or z for x. If there are several objects, then the centroid of the entire system is given by

where n is the number of objects in the system. This equation can be simplify as

where is the centroid location of the i^th object, and Q_i is the length, area, or volume of the ith object, depending on the type of centroid.

For a system of lines, the coordinates of the centroid are

Here and are the centroid coordinates of the ith line, and L_i is the length of the ith line.

For a system of objects, the coordinates of the area centroid are

Here and are the area centroid coordinates of the ith object, and A_i is the area of the ith object.

For a system of objects, the coordinates of the volume centroid are

Here and are the volume centroid coordinates of the ith volume, and V_i is the volume of the ith object.

If an object or system of objects has a cutout or hole, then the centroid of the system can be found by considering the cutout or hole as a negative area, volume, or line length.

For example, if a system consists of a cube with a centroid at x₁, y₁, z₁ and a volume of V₁; and a hole within the cube that has a centroid at x₂, y₂, z₂ and a volume of V₂; then the coordinates of the centroid for the system are