Free · Force, power, and torque converters

Shaft Torque, RPM, Kilowatts & Horsepower

Relate steady shaft torque and rotation rate to mechanical power, retaining metric and customary torque and horsepower choices.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For torque 100 N·m at 3,000 rpm, shaft power is 10π kW, approximately 31.416 kW. The calculation uses the exact radians-per-revolution relationship.

Power (W) = torque (N·m) × angular speed (rad/s) = torque × rpm × 2π/60

Worked example

Enter these known values and leave the other values blank.

Shaft torque magnitude
100 N·m
Rotational speed
3000 rpm
Mechanical shaft power
31.416 kW
Equivalent horsepower unit
42.13 hp(l)

Assumptions and limitations

  • Torque, rotation speed and power are positive magnitudes for steady rotation. This tool does not model transient energy storage or signed regenerative power.
  • The result is mechanical power at the shaft where torque is specified. Electrical input power requires efficiency and other losses to be considered separately.
  • Horsepower definitions differ. Mechanical horsepower is exactly 550 ft·lbf/s; metric horsepower is 75 kgf·m/s; the electrical and boiler choices are other unit conventions. A thermal boiler-horsepower conversion is not a prediction of usable shaft output.

Common questions

Why can horsepower differ for the same power?

Mechanical, metric, electrical and boiler horsepower are differently sized units. Select the convention used in the specification you are comparing.

Why does doubling RPM double power at fixed torque?

At constant torque, twice the angular distance per second means twice the mechanical work per second.

References

Bookify uses the exact factor 2π/60 between RPM and radians per second instead of the captured rounded torque-to-power divisor. The boiler-horsepower selector uses the NIST tabulated 9809.5 watts per unit instead of the captured 9812.5-watt value. Pound-force feet use the exact international pound and foot with standard gravity. Mechanical horsepower uses exactly 550 foot-pounds-force per second instead of a rounded factor. The power unit uses the International Table BTU per hour consistently with the reviewed energy convention. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor.

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