 Welcome to Calculating Horsepower, RPM and Torque. There may be times when you, as a technician, will need to size a motor for an application. This will require selecting the correct horsepower based on RPM and torque requirements. Horsepower was devised by James Watt as a standard for comparing the power of his early steam engines. He found that the average horse could pull 330 pounds, a distance of 100 feet in one minute, which equals 33,000 foot pounds per minute. In electrical terms, one horsepower is equal to 746 watts. Torque T equals force times radius is the twisting action developed from a rotating shaft. Force, usually expressed in foot pounds or inch ounces, is present at the radius, the distance from the center of the twisting action. If the force at this point is 3 pounds and the radius is 2 feet, Torque equals 3 pounds multiplied by 2 feet or 6 foot pounds. The circumference of a circle is equal to pi times the diameter, c equals pi d. Since diameter equals 2 times the radius, circumference equals 2 pi r. The radius from c equals 2 pi r has already been incorporated into the horsepower formula through the formula for torque. Torque equals force times the radius. Regarding RPM or revolutions per minute, one revolution is equal to 360 degrees. The circumference of a circle, c equals pi d equals 2 pi r. Expressed in radians, 360 degrees is equal to 2 pi radians. A radian is equal to approximately 57.296 degrees. Therefore, 2 pi times 57.296 degrees equals 360 degrees. In summary, horsepower equals the quantity 2 pi times torque times RPM divided by 33,000. Where 2 pi equals radians in a full revolution, t equals torque in foot pound units, which equals force times radius, and RPM equals revolutions per minute. When using the horsepower formula, you must first convert all measurements to feet and pounds. Torque for a given object will not always be stated in foot pounds. Usually, the dimensions of a pulley, sheave, and motor shaft are given in inches, so torque, t, will be stated as inch pounds. Since torque in the horsepower formula is in foot pounds, all units must first be converted to foot pounds. In addition to inch pounds, you may also find torque stated in inch ounces or foot ounces. Being able to convert these units to the standard foot pounds is essential when calculating horsepower. There are two ways to convert non-standard torque units to foot pounds. The first method is to convert all torque units to foot pounds and then insert that number into the horsepower formula. This table shows how to convert torque given in different units to foot pounds. For instance, if torque equals 24 inch pounds, you would divide 24 inch pounds by 12, which equals 2 foot pounds. We would then use that number in the formula for t. The second method for making the conversion is to perform the division within the horsepower formula. Looking at the same problem we just solved using the first method, if torque equals 24 inch pounds, we would use 24 inch pounds for torque and 12 multiplied by 33,000 as the denominator. In some situations, you might have to solve for rpm or torque when horsepower is known. Here are the formulas. Solving for rpm. rpm equals horsepower multiplied by 33,000 divided by the quantity 2 pi multiplied by torque. Solving for t. t equals horsepower multiplied by 33,000 divided by the quantity 2 pi multiplied by rpm. You have completed calculating horsepower, rpm, and torque. You are now more prepared to verify that the motor you're using in a given application with specific torque and rpm requirements is correct.