 The losses in surface area and volume on the inner side of the tube exactly cancel out the gains on the outer side.Expressing the surface area and the volume by the distance of an outermost point on the surface of the torus to the center, and the distance of an innermost point (so that and ), yields

As a torus is the product of two circles, a modified version of the spherical coordinate system is sometimes used.In traditional spherical coordinates there are three measures, , the distance from the center of the coordinate system, and and , angles measured from the center point.