The Center of Mass (center of gravity) of a solid is similar to the Centroid of Solid. However, calculating the centroid involves only the geometrical shape of the solid.

The center of gravity will equal to the centroid if the body is homogenous i.e. constant density.

Integration formulas for calculating the Center of Mass are:

The perpendicular distance in the x direction from the yz-plane to the Center of Mass is Cx The perpendicular distance in the y direction from the zx-planeto the Center of Mass is Cy The perpendicular distance in the z direction from the xy-plane to the Center of Mass is Cz The coordinates of the Center of Mass are (Cx , Cy , Cz).

When calculating the centroid of a complex shape. Divide the shape up into a combination of known shapes. Then use the the following formula:

The perpendicular distance in the x direction from the ys-plane to the Center of Mass is Cx The perpendicular distance in the y direction from the zx-plane to the Center of Mass is Cy The perpendicular distance in the z direction from the xy-plane to the Center of Mass is Cz The coordinates of the Center of Mass are (Cx , Cy , Cz)

The centroid location of many common shapes can be found through the Properties of Solids page which also includes Volume, Mass Moments of Inertia, Mass Polar Moments of Inertia, and Mass Radius of Gyration.