Shaft Power Calculator Formula

Understand the math behind the shaft power calculator. Each variable explained with a worked example.

Use the Shaft Power Calculator

Formulas Used

Shaft Power

power_w = torque * omega

Shaft Power

power_kw = torque * omega / 1000

Shaft Power

power_hp = torque * omega / 746

Variables

VariableDescriptionDefault
torqueShaft Torque (T)(N-m)100
rpmRotational Speed(RPM)1500
omegaDerived value= 2 * pi * rpm / 60calculated

How It Works

Shaft Power from Torque and Speed

Rotational power is the product of torque and angular velocity.

Formula

P = T omega = T (2 pi N / 60)

where T is torque in N-m, N is speed in RPM, and P is power in watts. Dividing by 1000 gives kilowatts. One horsepower equals 746 watts.

Worked Example

A shaft transmitting 100 N-m torque at 1500 RPM.

torque = 100rpm = 1500
  1. 01omega = 2 x pi x 1500 / 60 = 157.08 rad/s
  2. 02P = 100 x 157.08 = 15,708 W = 15.71 kW
  3. 03P = 15,708 / 746 = 21.06 hp

Frequently Asked Questions

What is the difference between shaft power and electrical power?

Shaft (mechanical) power is what the motor delivers at its shaft. Electrical power input is higher due to motor losses. Motor efficiency = shaft power / electrical input power, typically 85-95%.

How do I measure shaft torque?

Shaft torque can be measured with a strain-gauge torque transducer, a reaction-force torque arm, or calculated from motor current draw and speed. Inline torque sensors are the most accurate method.

Can I use this for pumps and compressors?

Yes. If you know the torque and speed of a pump or compressor shaft, this formula gives the mechanical power input to the machine.

Learn More

Guide

How to Calculate Gear Ratios: Complete Engineering Guide

Learn how to calculate gear ratios for spur gears, compound gear trains, and planetary systems. Covers speed, torque, and efficiency relationships with practical examples.

Ready to run the numbers?

Open Shaft Power Calculator