Horsepower From Torque and RPM: Why 5252 Is In Every Formula

Torque is the twist. Horsepower is how fast you can keep producing that twist. Most of what is confusing about the number follows from those two sentences, including the odd 5252 in the denominator.

The 5252 in the formula

James Watt defined one horsepower as 33,000 foot-pounds of work per minute. Converting rotation into that unit means dividing by 2 pi, and 33,000 / 6.2832 = 5252, so hp = torque x rpm / 5252 with torque in pound-feet.

Run it forwards: 300 lb-ft at 5,000 rpm gives 300 x 5000 / 5252 = 285.6 hp. Run it backwards: an engine quoted at 180 hp at 6,000 rpm must be making 180 x 5252 / 6000 = 157.6 lb-ft there.

Torque and power curves on the same chart always cross at 5,252 rpm, because that is the one engine speed where the two numbers are equal by definition. If a dyno plot shows them crossing elsewhere, the axes are scaled differently.

Metric horsepower, PS and kilowatts

Mechanical horsepower is 745.7 watts. Metric horsepower, written PS in Germany or CV in France, is 735.5 watts, about 1.4% smaller. A car advertised at 200 PS is 197 hp. A 150 kW electric motor is 201 hp. UK brochures often quote all three, so the same car can be a 148 hp, 150 PS or 110 kW model depending on the page.

Estimating horsepower from performance

Trap speed and elapsed time

Two long-standing drag racing estimates work from a timing slip. Using trap speed, hp is roughly weight x (mph / 234) cubed, so a 3,500 lb car crossing the line at 100 mph gives 3,500 x 0.078 = 273 hp.

Using elapsed time, hp is roughly weight divided by (ET / 5.825) cubed. The same 3,500 lb car running 13.5 seconds gives 3,500 / 12.45 = 281 hp. The two landing within 3% of each other is a good sign; when they disagree badly, something about the run was off, usually traction.

Both assume a clean pass. A headwind, a slipping clutch or a missed shift all move the answer, and neither formula knows.

Horsepower away from the racetrack

The unit turns up in pumps and compressors too. Hydraulic horsepower is flow in gallons per minute times head in feet, divided by 3960, so a pump moving 50 gpm to a height of 100 feet needs 1.26 hp of useful output, or about 1.94 hp at the shaft once you allow 65% efficiency. That is why you buy the 2 hp unit.

Electrical ratings convert at 746 watts per horsepower. A 1.5 kW garage compressor is a 2 hp compressor; a 2.2 kW motor is 3 hp.

Using the horsepower calculator

Pick the method that matches the numbers you have: torque and rpm, weight and trap speed, or watts.

Torque and peak rpm come from the manufacturer's spec sheet or a dyno printout. Kerb weight is on the V5C in the UK and the driver's door jamb sticker in the US, but for the trap speed method add the driver and the fuel, because the timing gear measured the car with both aboard. A 180 lb driver alone shifts a 3,500 lb estimate by about 14 hp.

Watch the torque units. One pound-foot is 1.3558 newton-metres, so a spec sheet quoting 400 Nm means 295 lb-ft. Feed the 400 straight into a formula expecting lb-ft and at 5,000 rpm it returns 381 hp instead of 281, inventing 100 hp that is not there. Running costs come off the same spec sheet, covered in calculating gas mileage.

Common questions

Is horsepower or torque more important for towing? Torque low in the rev range, plus gearing. A diesel making 400 lb-ft at 1,800 rpm is only making 137 hp, but that is where towing happens.

Why does my car feel slower than its horsepower suggests? Weight. A 300 hp SUV at 4,400 lb has about 136 hp per ton; a 250 hp coupe at 2,800 lb has 179. The smaller brochure number wins.

What is the difference between wheel and crank horsepower? Crank figures are measured at the engine, wheel figures after the driveline takes its cut. Losses are commonly quoted around 10 to 15% for a manual rear-drive car, higher for automatics and all-wheel drive.

Does altitude change horsepower? For a naturally aspirated engine, yes, roughly 3% per 1,000 feet of elevation. Turbos lose much less because the compressor makes up for the thinner air. Fuel use shifts too, which the fuel cost calculator guide covers.