Motor Mechanical Power
P = τ × ω
Quick answer
This calculator solves P = τ × ω for Power. With Torque 1 N·m, Angular Velocity 300 rad/s, the result is 0.3 kW. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Mechanical power output of a motor is the product of torque and angular velocity. This is the rotational analog of linear power P = F × v. To convert from RPM to rad/s, multiply by 2π/60. For example, a motor spinning at 3000 RPM has ω = 314.16 rad/s. If it produces 0.5 N·m of torque, the mechanical output power is 157 W. The electrical input power is higher than this due to losses (copper losses in windings, iron losses in the core, friction, and windage), with typical motor efficiencies ranging from 60-95% depending on the motor type and size.
Variables
- P — Mechanical power output (W)
- τ — Torque (N·m)
- ω — Angular velocity (rad/s)
Practical Notes
1 horsepower ≈ 746W. DC motor power curves show that torque is maximum at stall (zero speed) and zero at no-load speed, while power peaks at approximately half the no-load speed. BLDC and stepper motors have different torque-speed characteristics. Always check that the motor driver can supply the stall current without damage.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| P | Power | W | µW, mW, W, kW |
| tau | Torque | N·m | N·m, mN·m |
| omega | Angular Velocity | rad/s | rad/s, RPM |
Step by step
- 1. What you know: Torque 1 N·m, Angular Velocity 300 rad/s
- 2. The relation: P = τ × ω
- 3. Substitute: tau = 1 N·m, omega = 300 rad/s
- 4. Result: Power = 0.3 kW
Worked examples
Minimum range
Given: Torque 5 mN·m, Angular Velocity 9.549 RPM
Result: Power = 5 mW
Low range
Given: Torque 50 mN·m, Angular Velocity 10 rad/s
Result: Power = 0.5 W
Typical
Given: Torque 1 N·m, Angular Velocity 300 rad/s
Result: Power = 0.3 kW
High range
Given: Torque 50 N·m, Angular Velocity 3000 rad/s
Result: Power = 150 kW
Maximum range
Given: Torque 500 N·m, Angular Velocity 30000 rad/s
Result: Power = 15000 kW
Solving for each variable
Solve for Power
Torque 5 mN·m, Angular Velocity 9.549 RPM → 5 mW
Solve for Torque
Power 10 mW, Angular Velocity 9.549 RPM → 10 mN·m
Solve for Angular Velocity
Power 10 mW, Torque 5 mN·m → 2 rad/s
How Power changes with Torque
| Torque (input) | Power (result) |
|---|---|
| 100 mN·m | 30 W |
| 0.25 N·m | 75 W |
| 0.5 N·m | 150 W |
| 0.75 N·m | 0.225 kW |
| 1 N·m | 0.3 kW |
| 1.5 N·m | 0.45 kW |
| 2 N·m | 0.6 kW |
| 4 N·m | 1.2 kW |
| 7 N·m | 2.1 kW |
| 10 N·m | 3 kW |
The same result in other units
| Unit | Value |
|---|---|
| mW | 300000 |
| W | 300 |
| kW | 0.3 |
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<p><a href="https://vbatpower.com/formulas/motor-power/">Motor Mechanical Power</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Motor Mechanical Power?
Use P = τ × ω. With Torque 1 N·m, Angular Velocity 300 rad/s, Power works out to 0.3 kW.
What is the formula for Motor Mechanical Power?
The formula is P = τ × ω. Mechanical power output of a motor is the product of torque and angular velocity.
How do you find Torque when you know the other values?
Rearrange for Torque: with Power 10 mW, Angular Velocity 9.549 RPM, Torque is 10 mN·m.
How do you find Angular Velocity when you know the other values?
Rearrange for Angular Velocity: with Power 10 mW, Torque 5 mN·m, Angular Velocity is 2 rad/s.
What units does Motor Mechanical Power use?
Power is shown in mW, W, kW. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Motors & Mechanical formulas →Need more features?
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