Orthodontic forces can be treated mathematically as vectors. When more than one force is applied to a tooth, the forces can be combined to determine a single overall resultant. Forces can also be divided into components in order to determine effects parallel and perpendicular to the occlusal plane, Frankfort horizontal, or the long axis of the tooth. Forces produce either translation (bodily movement), rotation, or a combination of translation and rotation, depending upon the relationship of the line of action of the force to the center of resistance of the tooth. The tendency to rotate is due to the moment of the force, which is equal to force magnitude multiplied by the perpendicular distance of the line of action to the center of resistance. The only force system that can produce pure rotation (a moment with no net force) is a couple, which is two equal and opposite, noncolinear but parallel forces. The movement of a tooth (or a set of teeth) can be described through the use of a center of rotation. The ratio between the net moment and net force on a tooth (M/F ratio) with reference to the center of resistance determines the center of rotation. Since most forces are applied at the bracket, it is necessary to compute equivalent force systems at the center of resistance in order to predict tooth movement. A graph of the M/F ratio plotted against the center of rotation illustrates the precision required for controlled tooth movement.