The one formula, and where 5252 comes from
Horsepower is not a number stored in the engine. It is torque multiplied by how fast that torque spins, scaled by 5252. That constant is 33,000 ÷ 2π, the definition of one horsepower (33,000 ft-lb per minute) converted to a per-revolution basis. Rearranged, torque = HP × 5252 ÷ RPM and RPM = HP × 5252 ÷ torque, so any two of the three values give you the third.
Why the two curves always cross at 5252 RPM
Below 5252 RPM the torque number is higher than the horsepower number; above it, horsepower is higher. They meet at exactly 5252 on every gasoline dyno chart, because that is where RPM ÷ 5252 equals 1.
Same 250 ft-lb of torque throughout. Horsepower rises with RPM and equals the torque figure exactly at 5252.
Quick reference
| Torque | RPM | Horsepower |
|---|---|---|
| 100 ft-lb | 4000 | 76 hp |
| 200 ft-lb | 5252 | 200 hp |
| 300 ft-lb | 3000 | 171 hp |
| 400 ft-lb | 6000 | 457 hp |
| 500 ft-lb | 1600 | 152 hp |
For newton-meters, swap 5252 for 9549. A shaft at 300 N·m and 4000 RPM makes 300 × 4000 ÷ 9549 = 126 hp.
What people get wrong
- More torque is not more power. Power depends on torque and RPM together. A low-revving engine can post big torque yet modest horsepower.
- The formula is universal. It applies to any rotating shaft — gas engines, electric motors, pumps, compressors. Only the constant changes with the units.
- Use torque at that specific RPM. Real engines have torque that varies across the rev range, which is why you read both curves off a dyno chart rather than trusting one peak number.
Common questions
What is the formula for horsepower from torque and RPM?
Horsepower equals torque in foot-pounds times RPM, divided by 5252. In metric, horsepower equals torque in newton-meters times RPM divided by 9549, and kilowatts is the same divided by 9549000.
Why is horsepower and torque always equal at 5252 RPM?
Because the constant 5252 is baked into the formula. When RPM equals 5252, the RPM-over-5252 term becomes 1, so the horsepower number matches the torque number. On any dyno chart the two curves cross at exactly 5252 RPM.
Can an engine have high torque but low horsepower?
Yes. A diesel making 500 ft-lb at 1200 RPM produces only about 114 hp, because power is torque times how fast that torque is delivered. The same 500 ft-lb at 5000 RPM would be about 476 hp.
