Torque to horsepower formula
This converts between rotational torque and power in either unit system. In imperial units divide torque times rpm by 5252 for horsepower; in metric, divide torque times rpm by 9549 for kilowatts.
Variables
| HP | Power (imperial) | horsepower |
| kW | Power (metric) | kilowatts |
| T | Torque (lb·ft for HP, N·m for kW) | lb·ft or N·m |
| N | Rotational speed | rpm |
Rearranged
T(N·m) = kW × 9549 / N
1 HP = 0.7457 kW
Worked example
A motor delivers 300 N·m at 2,000 rpm.
Metric power: 300 × 2,000 / 9549 = 62.8 kW.
In imperial that is about 84 horsepower.
The two constants play the same role in each system: 5252 for pound-feet and horsepower, 9549 for newton-metres and kilowatts. To go the other way, multiply power by the constant and divide by rpm to recover torque. One horsepower equals about 0.746 kilowatts.
Need the derivation or torque basics?
See the Horsepower Formula and the Torque Formula.
Imperial and metric constants
The imperial constant 5252 converts pound-feet and rpm to horsepower; the metric constant 9549 converts newton-metres and rpm to kilowatts. Both come from the same physics, power equals torque times angular velocity, with the unit conversions folded in. Use the constant that matches the units of your torque value.
Converting both directions
To find power from torque, multiply torque by rpm and divide by the constant. To find the torque a machine must produce for a target power, multiply power by the constant and divide by rpm. This is how you size a motor: pick the power and speed, then check the torque the shaft and drivetrain must carry.
FAQ
How do I convert torque to horsepower?
Multiply torque in pound-feet by rpm and divide by 5252. For kilowatts, use torque in newton-metres and divide by 9549.
What is the metric version of 5252?
It is 9549, used with newton-metres and rpm to give power in kilowatts.
How many kilowatts is one horsepower?
About 0.7457 kilowatts. To convert horsepower to kilowatts, multiply by roughly 0.746.