The term "horsepower" was invented 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[5]. 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, thus in a minute the horse travelled 2.4 × 2π × 12 feet. Watt judged that the horse could pull with a force of 180 pounds (just assuming that the measurements of mass were equivalent to measurements of force in pounds-force, which were not well-defined units at the time). So:
This was rounded to an even 33,000 ft·lbf/min.
Others recount that Watt determined that a pony could lift an average 220 pounds 100 feet (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.
Put into perspective, a healthy human can produce about 1.2hp briefly and sustain about 0.1hp indefinitely, and trained athletes can manage up to about 0.3 horsepower for a period of several hours.
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 to a horse proved to be an enduring marketing tool.