Horsepower formula
Horsepower measures the rate of doing work. For a rotating shaft it comes straight from torque and speed: multiply torque in pound-feet by rpm and divide by the constant 5252.
Variables
| HP | Power | horsepower |
| T | Torque | lb·ft |
| N | Rotational speed | rpm |
| 5252 | Unit constant (33000 / 2π) | – |
Rearranged
N = HP × 5252 / T
Worked example
An engine makes 200 lb·ft of torque at 3,000 rpm.
Apply the formula: 200 × 3,000 / 5,252 = 114.
Power rises with both torque and speed, so a small engine spinning fast can match a large one turning slowly. The constant 5252 carries the unit conversions for pound-feet, rpm, and horsepower, and it is the rpm where torque and horsepower curves always cross.
Converting to metric or back to torque?
See the Torque to Horsepower Formula and the Torque Formula.
Where 5252 comes from
One horsepower is 33,000 foot-pounds per minute. Converting torque and rpm into that unit involves multiplying by two pi, for radians per revolution, and dividing by 33,000. The constants collect into 33,000 over two pi, which is 5252. It is not arbitrary; it is the bookkeeping that links pound-feet and rpm to horsepower.
Torque vs horsepower
Torque is the twisting force available now; horsepower is how fast work gets done, combining torque with speed. A tractor has huge torque at low speed for pulling; a race engine makes its horsepower by revving high. Because of the 5252 constant, the two curves on a dyno chart always intersect at 5252 rpm.
FAQ
What is the horsepower formula?
Horsepower equals torque in pound-feet times rpm divided by 5252. Rearranged, torque equals horsepower times 5252 divided by rpm.
Why is the number 5252 used?
It equals 33,000 divided by two pi, the constant that converts pound-feet and rpm into horsepower. It is also where torque and power curves cross.
Can low torque still make high horsepower?
Yes. Because power depends on speed too, a modest torque at very high rpm can produce large horsepower.