How to use the horsepower and torque calculator
- Solve for: choose Horsepower, Torque or RPM, whichever you want to find.
- Power unit and Torque unit: pick hp, kW or PS, and lb-ft or N·m. Numbers you already typed convert when you switch.
- Fill in the two fields that remain, such as Torque and Engine speed (RPM) when solving for horsepower.
- Read the answer under Your results. It also lists power and torque in every unit.
How the numbers are worked out
Power is torque times rotational speed. With torque in lb-ft and speed in RPM, horsepower = torque × RPM ÷ 5252.11, where 5252.11 is 33,000 ÷ 2π; the familiar 5252 is that value rounded (Wikipedia, Horsepower). The calculator does the sum in SI units, watts = N·m × RPM × 2π ÷ 60, and converts with the factors in NIST SP 811, Appendix B.8: 1 hp = 745.6999 W, 1 PS = 735.49875 W and 1 lb-ft = 1.355818 N·m. Solving for torque or RPM rearranges the same equation. The hp used here is the mechanical horsepower of 550 foot-pounds per second.
Worked example with the starting numbers
With Solve for set to Horsepower, Torque at 350 lb-ft and Engine speed at 4,500 RPM, the result is 350 × 4,500 ÷ 5,252.11 = 299.9 hp. That is 223.6 kW or 304.0 PS, and the 350 lb-ft is 474.5 N·m. Switch Solve for to RPM with 300 hp and 350 lb-ft and the answer is 4,502 RPM.
Limits and edge cases
- Both values must come from the same RPM. An engine's peak torque and peak power happen at different speeds, so combining the two peak figures gives a meaningless RPM.
- Every entered value must be between 0.001 and 1,000,000,000. Zero, negative and blank entries show a message instead of a result.
- The result is a calculation, not a measurement. It ignores drivetrain loss, altitude and temperature.
- For unit conversions alone, use the torque unit converter or the power converter. To turn engine speed into road speed, try the gear ratio calculator.
Horsepower and torque questions
How do you calculate horsepower from torque and RPM?
Multiply torque in lb-ft by engine speed in RPM and divide by 5,252. For 350 lb-ft at 4,500 RPM that is 350 × 4,500 ÷ 5,252.11 = 299.9 hp. In metric units, power in kW equals torque in N·m times RPM divided by 9,549.3.
Where does 5252 come from?
One horsepower is defined as 33,000 foot-pounds of work per minute, and one turn of the crankshaft at 1 lb-ft of torque does 2π foot-pounds of work. So 33,000 ÷ 2π = 5,252.11 is the RPM at which 1 lb-ft of torque equals 1 hp.
Do horsepower and torque always cross at 5252 RPM?
On a chart that plots hp and lb-ft on the same scale, yes, because the formula makes the two numbers equal at 5,252 RPM. Below that speed the torque number is higher, above it the horsepower number is higher. In kW and N·m the lines cross at about 9,549 RPM, so the crossing point comes from the units, not from the engine.
What is the difference between hp and PS?
Mechanical horsepower (hp) is 745.7 watts. Metric horsepower (PS) is 735.5 watts, about 1.4% smaller, so a car rated at 300 PS makes about 296 hp. The kW rating is the SI unit and is used for the same engines in many countries.
Is wheel horsepower the same as engine horsepower?
No. Engine ratings are measured at the crankshaft. A chassis dynamometer measures at the wheels, after losses in the transmission and driveline, so wheel figures are lower. This calculator only converts the values you give it and does not estimate drivetrain loss.
Sources: Wikipedia, Horsepower; NIST, Guide for the Use of the International System of Units, Appendix B.8.