The horsepower of an engine is equal to the torque multiplied by the rpm and divided by 5,252. This is because power is equal to force times distance divided by time, and 1 horsepower is equal to 33,000 foot-pounds of work per minute.
Since torque is equal to force multiplied by radius, and the distance per minute of an engine's work is equal to the radius times two multiplied by pi and multiplied yet again by the rpm, the power of an engine's work is equal to the force times the distance per minute. Upon dividing both sides by 33,000 to arrive at the horsepower of the engine's output, the number 5,252 appears as a scalar variable that unites the relative values of the units.
As an example of the results that these equations imply, a single horsepower engine spinning at 3,450 rpm produces 18 pound-feet of torque, while the same engine spinning at 500 rpm produces 189 pound-feet of torque. A 10-horsepower engine spinning at 3,450 rpm produces 183 pound-feet of torque, while the same power at 500 rpm produces 1260 pound-feet of torque. One hundred horsepower produced by an engine spinning at 3,450 rpm produces 1,827 pound-feed of torque, and a 600-horsepower engine spinning at 500 rpm produces 75,629 pound-feet of torque.