What is the ‘horsepower’ unit of measurement based on?


Horsepower (HP) is the name of several units of measurement of power. The most common definitions equal between 735.5 to 746 watts. The horsepower is not recognized in the International System of Units (SI).

The horsepower was originally defined to compare the output of steam engines with the power of draft horses. The unit was widely adopted to measure the output of piston engines, turbines, electric motors, and other machinery. The definition of the unit varied between geographical regions. Most countries now use the SI unit watt for measurement of power.

The definition of the horsepower also has varied between different applications:

    • The mechanical horsepower of 550 foot-pounds per second is approximately equivalent to 745.7 watts.

    • The metric horsepower of 75 kgf-m per second is approximately equivalent to 735.499 watts.

    • The boiler horsepower is used for rating steam boilers and is equivalent to 34.5 pounds of water evaporated per hour at 212 degrees Fahrenheit, or 9,809.5 watts.

    • One horsepower for rating electric motors is equal to 746 watts.

    • The Pferdestärke (German translation of horsepower) is a name for a group of similar power measurements used in Germany around the end of the 19th century, all of about one metric horsepower in size.

  • The Royal Automobile Club (RAC) horsepower or British tax horsepower is an estimate based on several engine dimensions.

The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner’s Friend: “So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, and for which there must be constantly kept ten or twelve horses for doing the same. Then I say, such an engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work…”

The idea was later used by James Watt to help market his improved steam engine. He had previously agreed to take royalties of one third of the savings in coal from the older Newcomen steam engines. This royalty scheme did not work with customers who did not have existing steam engines but used horses instead. Watt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute). The wheel was 12 feet in radius, therefore the horse travelled 2.4 × 2π × 12 feet in one minute. Watt judged that the horse could pull with a force of 180 pounds. So:

formula for horsepower

This was rounded to an even 33,000 ft·lbf/min.

Others recount that Watt determined that a pony could lift an average 220 lbf (0.98 kN) 100 ft (30 m) per minute over a four-hour working shift. Watt then judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft·lbf/min figure.

Engineering in History recounts that John Smeaton initially estimated that a horse could produce 22,916 foot-pounds per minute. John Desaguliers increased that to 27,500 foot-pounds per minute. “Watt found by experiment in 1782 that a ‘brewery horse’ was able to produce 32,400 foot-pounds per minute.” James Watt and Matthew Boulton standardized that figure at 33,000 the next year.

Most observers familiar with horses and their capabilities estimate that Watt was either a bit optimistic or intended to underpromise and overdeliver; few horses can maintain that effort for long. Regardless, comparison with a horse proved to be an enduring marketing tool.

A healthy human can produce about 1.2 hp briefly (see orders of magnitude) and sustain about 0.1 hp indefinitely; trained athletes can manage up to about 2.5 hp briefly and 0.3 hp for a period of several hours.

Horsepower from a horse

R. D. Stevenson and R. J. Wassersug published an article in Nature 364, 195-195 (15 July 1993) calculating the upper limit to an animal’s power output. The peak power over a few seconds has been measured to be as high as 14.9 hp. However, for longer periods, an average horse produces less than one horsepower.