Horsepower calculator: torque, rpm and quarter-mile

Multiply torque in lb-ft by rpm and divide by 5,252. An engine making 350 lb-ft at 5,600 rpm produces 350 × 5,600 ÷ 5,252 = 373 hp. The constant comes from James Watt's horsepower of 33,000 foot-pounds per minute: a 1 lb-ft torque does 2π foot-pounds of work per revolution, and 33,000 ÷ 2π = 5,252.1. In metric units, kW = N·m × rpm ÷ 9,549.

At 5,252.1 rpm the conversion factor is exactly 1, so the number of horsepower equals the number of lb-ft. Below that speed the torque figure is larger, and above it the horsepower figure is larger. On a dyno chart drawn in hp and lb-ft on the same scale, the two curves always meet at 5,252 rpm; drawn in kW and N·m they cross at 9,549 rpm instead.

Hale's formulas give hp = weight × (trap mph ÷ 234)³ or hp = weight ÷ (ET ÷ 5.825)³, with weight in pounds including the driver. A 3,500 lb car trapping at 105 mph comes out at 3,500 × (105 ÷ 234)³ = 316 hp. Jeff Lucius's comparison of 243 Road & Track tests found trap speed predicts power better than ET, because launch and traction affect the time far more than the speed.

Crank (brake) horsepower is measured at the engine's output shaft; wheel horsepower is what reaches the tires on a chassis dynamometer after the transmission, driveshaft and differential take their share. 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. Road & Track measured a 500 hp Mustang at 421 to 465 wheel hp on four different dynos.

Mechanical horsepower is 550 ft·lbf per second, or 745.7 watts (NIST SP 811). Metric horsepower (PS, CV or ch) is 75 kgf·m per second, 735.5 watts, so 1 hp = 1.0139 PS. European makers quote PS or kW: 300 PS is 296 hp or 220.6 kW. Electric horsepower, used for motors, is defined as exactly 746 watts.

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 9 worked examples whose answers come from independent sources; for example, “350 lb-ft at 5,600 rpm” is checked against Python decimal with 2π exact: 350 × 5600 × 2π / 33000 = 373.183 hp (Inch Calculator's worked example gives 373.19 with the rounded 5,252); × 0.85 = 317.206.

NIST SP 811 Appendix B.8 — horsepower (550 ft·lbf/s) = 745.6999 W; metric horsepower = 735.4988 W; Jeff Lucius, stealth316.com — Calculate horsepower, ET and MPH (Huntington, Fox, Hale and LRT formulas with fit to 243 Road & Track tests); G. T. Fox, “On the physics of drag racing”, American Journal of Physics 41, 311 (1973); Garrett Motion — Crank vs wheel horsepower (drivetrain loss rule of thumb).