Rotational Power Calculator

Physics overview

What is rotational power?

Rotational power measures how quickly rotational work is performed. It depends on the torque applied to an object and its angular velocity.

Formula

Rotational power formula

• P is rotational power in watts.
• τ is torque in newton-meters.
• ω is angular velocity in radians per second.

Worked example

A shaft produces 12 N·m of torque at 5 rad/s

1. Write the formula: P = τω.
2. Substitute the values: P = 12 × 5.
3. Calculate the power: P = 60 W.

Rearranged equations

Solve for torque or angular velocity

Physical relationship

Torque and speed both affect power

Rotational power increases when torque increases, angular velocity increases, or both increase. A system can produce the same power using high torque at low speed or lower torque at higher speed.

Units

Standard SI units

Use watts for power, newton-meters for torque, and radians per second for angular velocity.

Real-world applications

Where rotational power is used

• Electric motors and generators.
• Vehicle engines and drive shafts.
• Turbines and industrial machinery.
• Gearboxes and transmission systems.
• Rotating laboratory equipment.

Calculation limits

Important assumptions

• Power, torque, and angular velocity must be greater than zero.
• Torque is assumed to act along the rotation axis.
• Angular velocity is treated as constant at the calculation point.
• Mechanical losses are not included.
• Units are not converted automatically.

Related tools

Continue your rotational analysis

Use the Torque Calculator to calculate torque, force, or lever arm distance.

Use the Angular Velocity Calculator to calculate angular velocity, angular displacement, or time.

Questions and answers

Rotational power calculator FAQ