Formula
Power is torque times angular speed. One horsepower is 33,000 foot-pounds per minute. Dividing by 2π, the radians in a turn, gives 5252.113. Kilowatts from newton-metres use 60,000 ÷ 2π, which is 9549.297. One mechanical horsepower is 0.74569987 kW. One PS is 0.73549875 kW.
hp = lb-ft × RPM ÷ 5252.113
kW = N·m × RPM ÷ 9549.297
τ = force × arm × sin(angle)
Four hundred pound-feet at 5,252.1 rpm is 400.0 hp. The curves cross there only when the chart is drawn in pound-feet and horsepower. A force square to a lever uses the full product. Thirty degrees keeps half of it, because the sine of 30° is ½. Crank torque and wheel torque differ by the gear and by the losses. Enter the figure you measured, at the RPM you measured it.
Worked examples
400 lb-ft at 5,252.113 rpm. 400.0 hp.
300 lb-ft at 4,000 rpm. About 228.5 hp.
450 hp at 6,500 rpm. About 363.6 lb-ft.
300 N·m at 3,000 rpm. About 94.25 kW, or 126.4 hp.
400 lb-ft. About 542.3 N·m. 50 lb at 2 ft, 90°. 100 lb-ft, 1,200 lb-in, about 135.6 N·m. 200 N at 0.3 m, 30°. 30.0 N·m. At 90° that arm is 60.0 N·m.
Reference
1 lb-ft = 1.3558179 N·m = 12 lb-in. 1 kgf·m = 9.80665 N·m. The divisors are 33,000 ÷ 2π and 60,000 ÷ 2π, rounded to three decimals.
Questions
How do you convert torque to horsepower?
Multiply pound-feet by RPM and divide by 5,252.113. Three hundred pound-feet at 4,000 rpm is about 228.5 hp. The same torque in newton-metres uses 9,549.297 to reach kilowatts.
How do you convert horsepower to torque?
Multiply horsepower by 5,252.113 and divide by RPM. Four hundred fifty horsepower at 6,500 rpm is about 363.6 lb-ft. Use the RPM where that horsepower happens, not the RPM of peak torque.
Why is the constant 5,252?
One horsepower is 33,000 foot-pounds per minute. A full turn is 2π radians, so 33,000 ÷ 2π is 5,252.113. Horsepower and pound-feet are equal at that RPM. Newton-metres and kilowatts do not cross there.
Is torque or horsepower more important?
They are the same relationship at one RPM. Torque is the twist. Horsepower is that twist times how fast the shaft turns. A gear multiplies torque and divides speed. The ratio that reaches the tire is what the car uses.
How do I convert pound-feet to newton-metres?
Multiply by 1.3558179. Four hundred pound-feet is about 542.3 N·m. Twelve pound-inches make one pound-foot. One kilogram-force metre is 9.80665 N·m.
How do you calculate torque from force and distance?
Torque is force times the lever arm times the sine of the angle between them. Fifty pounds at two feet, square to the arm, is 100 lb-ft. At 30 degrees the sine is one half, so the torque is half of the square case.
Can I use peak torque and the RPM of peak horsepower together?
No. The formula wants both numbers at the same RPM. Peak torque and peak horsepower are usually at different speeds. Pairing them invents an engine.
Sources
- James Watt’s horsepower is 33,000 foot-pounds per minute. Dividing by 2π gives the 5,252.113 used here. The metric divisor 9,549.297 is 60,000 ÷ 2π, for newton-metres and kilowatts.
- NIST Special Publication 811. One mechanical horsepower is 0.74569987 kW. The pound-foot to newton-metre factor used here is 1.3558179. Standard gravity, for the kilogram-force, is 9.80665 m/s².
- Torque as force times lever arm times the sine of the included angle is the definition in introductory mechanics. It is not a fastener preload. For bolt tightening specs, follow the manufacturer's torque values. Engine RPM at a road speed is the gear ratio calculator.