Mechanical vs Electrical Power
Two Forms of the Same Thing
Compare Power TypesAn electric motor converts electrical power to mechanical power; a generator does the reverse. Both measure the same fundamental quantity—the rate of energy transfer—but use different formulas and units. Understanding both helps when sizing motors, generators, and power systems.
Mechanical Power
Definition
Mechanical power is the rate of doing mechanical work—moving objects, rotating shafts, lifting loads.
Formulas
- Rotational: P = τ × ω (torque × angular velocity)
- Linear: P = F × v (force × velocity)
- Imperial: HP = (Torque × RPM) / 5,252
- Metric: kW = (Torque × RPM) / 9,549 (torque in Nm)
Common Units
- Watts (W), kilowatts (kW) - SI
- Horsepower (hp) - Imperial/US
- Metric horsepower (PS) - Europe
Electrical Power
Definition
Electrical power is the rate of electrical energy transfer through a circuit.
Formulas
- Basic: P = V × I (voltage × current)
- Resistive: P = I²R = V²/R
- AC (single phase): P = V × I × PF (power factor)
- AC (three phase): P = √3 × V × I × PF
Common Units
- Watts (W) - real power
- Volt-amps (VA) - apparent power
- Volt-amps reactive (VAR) - reactive power
Conversion Between Forms
Electric Motor
Converts electrical power to mechanical power:
- Input: Electrical (V × I × PF)
- Output: Mechanical (Torque × Speed)
- Efficiency: 85-98% typical
Output power = Input power × Efficiency
Generator
Converts mechanical power to electrical power:
- Input: Mechanical (engine, turbine)
- Output: Electrical (V × I)
- Efficiency: 90-98% typical
Comparison Table
| Aspect | Mechanical Power | Electrical Power |
|---|---|---|
| What flows | Force through distance | Electrons through conductor |
| Variables | Torque, speed (RPM) | Voltage, current |
| Traditional unit | Horsepower | Watts |
| Measured with | Dynamometer | Power meter |
| Transmission | Shafts, gears, belts | Wires, transformers |
| Losses from | Friction, heat | Resistance, reactance |
The Universal Unit: Watts
Both mechanical and electrical power can be expressed in watts:
- 1 watt = 1 joule/second
- 1 watt = 1 N·m/s (mechanical)
- 1 watt = 1 V·A (electrical, DC or unity PF)
This equivalence enables direct comparison and conversion calculations.
Conversion Reference
- 1 hp = 745.7 W
- 1 kW = 1.341 hp
- 1 BTU/hr = 0.293 W
Practical Applications
Motor Selection
Calculate mechanical load requirements, add safety margin, account for efficiency, specify electrical requirements.
Generator Sizing
Total electrical load (kW), divide by generator efficiency, match to prime mover (engine) mechanical output.
Power Transmission
Electrical transmission is more efficient over distance than mechanical (no friction losses in wires vs. shafts).
Conclusion
Mechanical and electrical power are the same fundamental quantity—rate of energy transfer—expressed differently. Mechanical power involves torque and speed; electrical power involves voltage and current. Motors and generators convert between forms with typical efficiencies of 85-98%. The watt is the universal unit that allows direct comparison between mechanical and electrical systems.