First, let us explain theoretically why motor volume can be used to estimate motor torque. Consider a cylindrical rotor with circumference width W and length L. The total tangential force developed by the rotor can be obtained from its surface area. Assume that an axial current of I = WA flows across the width W, where A is the current per unit width. All of this current is exposed to a radial magnetic flux density B. The tangential force is therefore given by B × WA × L, which is the magnetic force formula F = BIL. Since the rotor surface area is WL, the force per unit area is F / (WL) = B × A. Thus, the product of these two specific loadings (magnetic loading and electrical loading) represents the average tangential stress on the rotor surface.
To obtain the total tangential force, we multiply this stress by the rotor cylindrical surface area. To obtain the total torque, we multiply the total force by the rotor radius. Hence, for a rotor of diameter D and length L, the total torque is
T =（ B A）×（π D L）× D / 2 = （ B A）D² L
This equation is very important. The term D²L is proportional to the rotor volume, and thus we see that for given specific magnetic loading B and electrical loading A, the torque of any motor is proportional to the rotor volume. We are free to choose a long, thin rotor or a short, fat rotor; however, once the rotor volume and the specific loadings are fixed, the torque is effectively determined. It is worth emphasizing that we do not need to focus on any particular type of motor – we are discussing torque generation from a completely general point of view. Essentially, the above conclusion reflects the fact that all electric motors are made of iron and copper; they differ only in how these materials are arranged. In practice, what matters is the overall volume of the motor, not just the rotor volume. Experience again shows that, regardless of motor type, there is a fairly close relationship between the overall volume and the rotor volume for motors of similar torque.
It can be stated boldly – and accurately – that the overall volume of a motor is determined by the torque it must produce: the larger the volume, the greater the torque. Of course, there may be exceptions to this rule, but as a general guideline for motor selection, it is very useful.