# Detail

# What's the difference between torque and horsepower?

What’s the difference between horsepower and torque? It’s a simple question that doesn’t have a very simple answer. In short, both terms are used as units that measure force, but we’ll dig a bit deeper into what exactly that means. Let’s begin with torque. Torque is a measure of force that can cause an object to rotate around an axis. It can be mathematically calculated as: torque = force (lbs) x distance (in or ft) x sin(Θ). The “Θ” is the angle at which the force is applied relative to the object receiving the force. The function “sin(Θ)” is a factor that has to do with trigonometry. That said, the simple explanation is that if the force is applied perpendicu-lar (i.e., 90°) to the object, the factor is “1” [because sin (90°) = 1]. If the angle changes to something less than or greater than 90°, then the factor becomes less than 1 (until it goes all the way to 0° or 180°, which would imply that the force is not being applied to the object anymore). To support that argument, the sin (0°) is zero, so mathematically the factor goes to zero (and so does the torque).

Power is related to torque based on the speed of the rotation of the axis. Mathematically, power is derived from torque by multiplying the torque (T) by the rotational speed and dividing that result by a constant. The constant varies depending on the units used (Imperial or metric). In the Imperial system, if the force (F) is in pounds (lbs) and the distance (d) is in feet (ft), then the torque is in foot-pounds (ft-lbf, ft-lbf or ft-lb), and if the power is in horsepower (hp), then the constant is 5252:

Power (hp)=(Torque (T)*Speed (RPM))/5252

So, is torque more important than power? It depends. What is the application? Is the torque more important to the application, or does the power matter more? That is the real question. Note that if the torque is constant, an increase in power results in an increase in speed (or the rate at which the process runs).

Let’s go through some examples.

In a constant-torque application like a conveyor or mixer, when the system is fully loaded – such as a conveyor fully loaded with aggregates in a mining application - there is a tremendous amount of torque needed to move the load. However, if you were only focusing on the power, the material could be fully unloaded with minimal power, but it would do so at a very low speed (see the formula above). If the torque is fixed (i.e., a fixed aggregate load on the conveyor) and the power is low, the speed will also have to be low (and it will take a very long time to unload the conveyor). Likewise, if the power is increased, the speed will also increase, and the conveyor can be unloaded more quickly.

Now, if you look at a constant-power application - like a winder in a pulp and paper application- the tension is critical. For example, in a manufacturing process that is making toilet paper, constant tension needs to be kept on the material, and it is necessary to control the rate at which the roll is being wound to control that tension. The tension in the web is a function of the speed and torque at the winder. As the winder roll gets larger in diameter, the speed must decrease, and the torque must increase to ensure that the power is constant (see the formula above).

The most important step is to understand your application. Torque is rotational force - the umph to get something going. If Torque is constant, power relates to speed (or the rate to complete work), which is very dependent on the task being completed.

To learn more about motors for variable-torque, constant-torque and constant-power applications, watch the ABB Baldor-Reliance inverter duty (ID) motors webinar series.