Library / Mechanical / MEC-04
Mechanical
Shaft power from torque and speed
Power transmitted by a rotating shaft.
- Ref
- MEC-04
- Rev
- v1
- Field
- Mechanical
- Result
- P [kW]
P in watts, T torque in N·m, ω in rad/s, N in rpm. Always convert the speed to rad/s first.
The power a shaft transmits is the torque it carries times how fast it turns. The same power can be a high torque at low speed or a low torque at high speed.
Calculator
- Angular speed ω157.1 rad/s
- Power in horsepower (metric)42.71 PS
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A gearbox trades torque for speed but cannot create power: halving the speed doubles the torque (minus losses).
- Torque and speed multiply, so both matter equally. The torque curve of an engine times the speed gives its power curve.
- Peak power does not occur at peak torque; it is usually at a higher speed.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kW) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T Torque | 5 to 5,000 N·m | 0.7854 | 785.4 | 784.6 | +10% | +10 % |
| N Shaft speed | 60 to 20,000 rpm | 1.257 | 418.9 | 417.6 | +10% | +10 % |
Sweep of Shaft speed
| Shaft speed (rpm) | Shaft power (kW) |
|---|---|
| 60 | 1.257 |
| 124 | 2.598 |
| 256.4 | 5.369 |
| 529.9 | 11.1 |
| 1,095 | 22.94 |
| 2,264 | 47.43 |
| 4,681 | 98.03 |
| 9,675 | 202.6 |
| 20,000 | 418.9 |
Sweep one variable
Variables and how each one contributes
Shaft power
What the equation gives you. Everything else feeds it.
Torque
Torque at the shaft. Directly proportional at constant speed.
Shaft speed
Revolutions per minute. Directly proportional at constant torque.
Worked example with the values above
- Convert speed: ω = 2π × 1,500 / 60 = 157.1 rad/s.
- P = Tω = 200 N·m × 157.1 rad/s = 31,420 W.
- In kilowatts, 31.42 kW.
Assumptions and limits
- Steady torque and speed.
- Power at the shaft where T is measured.
- ω in rad/s.
Common mistakes
- Using rpm directly in place of rad/s.
- Mixing power at the engine with power at the wheels.
- Forgetting that the answer is in W before dividing by 1000 for kW.
Statistics and uncertainty
Relative errors combine as δP/P ≈ √[(δT/T)² + (δN/N)²]. Speed is easy to measure accurately, so the torque measurement normally dominates the uncertainty on a dynamometer.
Where it is used
- Sizing motors and engines.
- Dynamometer testing.
- Gear train and transmission design.
Maths you need
- Angular speed: convert rpm to rad/s
- Torque: turning moment in N·m