# How to Calculate Shaft Horsepower From Torque

by Richard RoweHorsepower is a mathematically derived number meant to give some perspective on how much work an engine can produce relative to a horse. The idea of horsepower is a fairly arbitrary one, and was originally developed by James Watt to market his new and improved steam engine. In actuality, an average horse can produce about 15 horsepower in short bursts and about 5 horsepower continuously. One horsepower is actually closer to the output of a medium-sized monkey.

#### Step 1

Multiply the engine RPM by the torque (measured in foot/pounds). Example: If you record 200 foot/pounds of torque at 5000 RPM, the result is 1,000,000.

#### Step 2

Record the number found in Step 1.

#### Step 3

Divide the number recorded by 5,252 to find the horsepower. Example: if you divide 1,000,000 by 5,252 you get 190, which is the engine's horsepower.

#### Step 4

Repeat steps 1 through 3 for as many RPM points as you'd like to measure, and record them on a graph, with RPM as the horizontal axis and horsepower as the vertical.

Draw a line connecting your data points, which will give you the engine's basic "horsepower curve."

#### Tips

- One horsepower is equal to between 735 and 746 watts for an electric motor. If you know the voltage and amperage input of an electric motor, multiply them together to get its wattage. Divide that number by 746 and you'll have the motor's theoretical horsepower. In reality, electric motors become less efficient with RPM (meaning that less of that input power gets transferred to output horsepower). If you have a table illustrating the motor's efficiency at any given RPM, multiply that number by whatever theoretical input you have.
- Example: If you have a motor that takes 112 volts and 80 amps, you have a theoretical output (if the motor were running at 100% efficiency) of 8,960. If your efficiency table shows that the motor is only 60% efficient at 5,000 rpm, then it's output at 5,000 rpm will be 5,276 watts. Divide that by 746, and you have an electric motor that produces 7.2 horsepower at 5,000 RPM.
- If you want to know that same motor's torque output, you need only switch around the basic horsepower equation to solve for torque. (Remember, "Horsepower = RPM x Torque / 5,252 ", so to solve for torque you would do it as " Torque = Horsepower x 5252 / RPM" ). In this example, you would multiply horsepower (7.2) by 5,252 (which equals 37,848), and then divide that by the RPM (5,000).
- What you wind up with is an electric motor that runs on 8,960 watts while producing 7.2 horsepower and 7.5 foot/pound of torque at 5,000 RPM.

#### Items you will need

- A Calculator
- Pencil
- Graph paper

- horse image by milemarsovac from Fotolia.com