Horsepower calculator: torque, rpm and quarter-mile

How to convert torque to horsepower

Multiply torque in lb-ft by engine speed in rpm and divide by 5,252: hp = lb-ft × rpm ÷ 5,252. An engine making 350 lb-ft at 5,600 rpm produces about 373.2 hp, or 278.3 kW. In metric units, kW = N·m × rpm ÷ 9,549. Take both figures at the same engine speed.

Where the 5,252 comes from

One mechanical horsepower is 33,000 ft·lbf of work per minute. A torque of 1 lb-ft does 2π ft·lbf of work per revolution, so 33,000 ÷ 2π = 5,252.11 turns lb-ft × rpm into horsepower. The metric constant is 60,000 ÷ 2π = 9,549.30.

The rounded 5,252 gives 373.19 hp for the example instead of 373.18 hp, a difference that only shows in the second decimal place.

How to convert horsepower to torque

Turn the formula around: lb-ft = hp × 5,252 ÷ rpm. Making 300 hp at 6,000 rpm takes 262.6 lb-ft; making the same 300 hp at 3,000 rpm takes twice as much, 525.2 lb-ft.

For metric figures, N·m = kW × 9,549 ÷ rpm. A rating of 300 PS (220.6 kW) at 6,000 rpm corresponds to 351.2 N·m, or 259.0 lb-ft.

hp, PS and kW are different units

• Mechanical horsepower (hp): 550 ft·lbf/s = 745.699872 W
• Metric horsepower (PS, also CV or ch): 75 kgf·m/s = 735.49875 W
• Kilowatt (kW): 1,000 W

So 1 hp = 1.0139 PS, and a European rating of 300 PS is 295.9 hp or 220.6 kW. The factors are from NIST SP 811.

Crank horsepower vs wheel horsepower

Crank horsepower is measured at the engine's output shaft. Wheel horsepower is what a chassis dynamometer reads after the transmission, driveshaft and differential take their share.

Wheel hp = crank hp × (1 − loss), so with a 15% loss, 373.2 crank hp becomes 317.2 hp at the wheels. Going the other way, crank hp = wheel hp ÷ (1 − loss).

A car that makes 300 wheel hp with a 15% loss has 300 ÷ 0.85 = 352.9 crank hp. Adding 15% to 300 gives 345 hp, which is too low.

Garrett Motion's rule of thumb is a 10% loss for front-wheel drive, 15% for rear-wheel drive and 20% for all-wheel drive, more with an automatic. Real losses are partly fixed and partly proportional, so any single percentage is an approximation.

How to estimate horsepower from a quarter-mile time

Drag-strip formulas link race weight, power and the time slip. Most online calculators use Hale's:

• From trap speed: hp = W × (mph ÷ 234)³
• From elapsed time: hp = W ÷ (ET ÷ 5.825)³

W is the weight in pounds with the driver aboard. A 3,500 lb car trapping at 105 mph gives 3,500 × (105 ÷ 234)³ = 316.2 hp.

Other published fits disagree. For the same car, Huntington (1958) gives 360.5 hp, Fox (2001) 333.0 hp and Jeff Lucius's best fit to 243 Road & Track tests 323.7 hp.

Trap speed tracks power more closely than elapsed time, because the launch and traction mostly affect the ET. Lucius found an R² of 0.93 for his trap-speed fit against 0.91 for ET.

The formulas estimate net engine (flywheel) horsepower. For a wheel figure, take off the drivetrain loss: 316.2 hp × 0.85 = 268.8 wheel hp.

Horsepower results side by side

Default is 350 lb-ft at 5,600 rpm. Metric torque is 400 N·m at 3,000 rpm, and wheel input is 300 wheel hp with a 15% loss. The hale trap and lrt trap rows are 3,500 lb at 105 mph by Hale's formula and by the Lucius best fit.

Common mistakes

• Mixing operating points. Peak torque arrives at a lower rpm than peak power, so peak torque × peak-power rpm overstates the engine.
• Treating PS as hp. 300 PS is 295.9 hp, so relabeling it overstates the power by 1.4%.
• Adding the loss to wheel horsepower. Divide by (1 − loss) instead.
• Using N·m with 5,252. That constant needs lb-ft; N·m pairs with 9,549 and gives kW.
• Using curb weight for a time slip. The formulas expect race weight with the driver.
• Using an eighth-mile or 0–60 time. The constants were fitted to quarter-mile results.

Units and measurement points

• Torque can be in lb-ft or N·m, and power in hp, kW or PS.
• Mark whether a torque or power figure was measured at the crank or at the wheels; drivetrain loss can be 0 to 60%.
• Race weight can be in lb or kg and trap speed in mph or km/h; ET is in seconds.

For unit conversions alone, use the kW to hp converter or the torque converter. The work, energy and power calculator finds power as work done per unit time.