# How to Calculate Horsepower & RPM ••• hamikus/iStock/GettyImages

A horsepower is a measure of unit for power, which defines how quickly work can be done by a force. The term horsepower was first introduced by Scottish Engineer James Watt. RPM is an acronym for revolution per minute. It describes circular motion, which happens as an object as turns around an axis. The force that causes the object to turn is called a torque. RPM is a useful speed measurement for motors, because it tells how quickly they can rotate when not under a load. To calculate horsepower, it is necessary to understand how it is related to torque and RPM.

Examine the definition of horsepower. In British units, it is 550 ft×lb / s, where ft is foot, lb is pound, and s is in seconds. It is sometimes abbreviated as hp.

Note the definition of torque. The size of the torque depends on how it is applied to the axis of rotation. The distance it is from the axis is important, as well as the angle it is applied at. For example, a wrench is most effective when the hand holding it is perpendicular to it. If the hand is held at a greater or lesser angle on the wrench, there is less force being applied and so it is harder to rotate an object, such as a bolt. In British units, torque is measured in lb×ft, and is usually denoted by the Greek letter τ.

Study the formula to convert horsepower between RPM. Work is equal to the torque multiplied by the time. The equation is therefore:

\text{power}=\tau\times\frac{\text{RPM}}{5252}

The constant 5252 is a result of converting RPM to radians per second, and of using the definition of horsepower.

Practice using the equation converting torque and RPM to horsepower. Do this by converting a given torque and RPM to that of horsepower. A torque of 120 lb × ft is applied so that a car’s drive shaft rotates at 3600 RPM. The horsepower delivered from the engine so that the shaft can power the wheels is:

\text{power}=(120\text{ lb}\times\text{ft})\times\frac{3600\text{ rpm}}{5252}=82\text{ hp}

Use the formula to convert a given horsepower and known torque to RPM. If the car engine delivers 72 hp to its wheels, and the RPM is 3600, then the torque used is:

\tau=\frac{(72\text{ hp})(52552)}{3600\text{ rpm}}=105\text{ lb}\times\text{ft}

#### Things You'll Need

• Horsepower to RPM conversion problem
• Calculator
• Introductory physics textbook

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