Understanding Power & Efficiency
Learn about mechanical power, electrical power, and efficiency calculations
Mechanical Power
Mechanical power is the rate at which work is done by forces in motion. Three common formulas relate power to force, torque, and work.
P = F × v
Power = Force × Velocity (linear motion)
P = τ × ω
Power = Torque × Angular Velocity (rotational)
P = W / t
Power = Work / Time (average power)
Electrical Power
Electrical power is the rate of energy transfer in circuits. DC and AC circuits have different considerations for power calculation.
P = V × I (DC)
Power = Voltage × Current
P = V × I × cos(φ) (AC)
Real power with power factor
P = I²R = V²/R
Power dissipation in resistance
AC Power Triangle
AC circuits have three types of power forming a right triangle. Only real power does useful work; reactive power oscillates.
- Apparent (S): V × I [VA] - Total power drawn
- Real (P): V × I × cos(φ) [W] - Useful power
- Reactive (Q): V × I × sin(φ) [VAR] - Oscillating power
- S² = P² + Q²
Efficiency Calculations
Efficiency measures how much input power becomes useful output. Real systems always lose some power to heat and other losses.
η = P_out / P_in × 100%
- • P_loss = P_in - P_out
- • η is always ≤ 100% in real systems
- • Series efficiency: η_total = η₁ × η₂ × η₃...
Power Unit Conversions
Power is measured in watts (W) in SI, but horsepower (hp) is common for engines and motors.
- • 1 kW = 1,000 W
- • 1 hp (mechanical) = 745.7 W
- • 1 hp (metric/PS) = 735.5 W
- • 1 kWh = 3.6 MJ (energy, not power)
Torque, Speed & Power
For rotating systems, power relates torque to angular speed. Gearboxes trade torque for speed at (nearly) constant power.
P = τ × ω
- • τ in N·m, ω in rad/s → P in W
- • RPM to rad/s: ω = RPM × 2π/60
- • Higher torque ⟷ lower speed at same power
Typical Efficiency Ranges
Electric Motors
70-98%
ICE Engines
20-40%
Transformers
95-99%
Solar Panels
15-25%
Educational Tool Only
This calculator uses simplified models for learning purposes. It is not suitable for industrial motor sizing, power system design, or safety-critical applications. Always consult qualified engineers for real-world electrical or mechanical power systems.
Frequently Asked Questions
Common questions about power calculations, efficiency, and unit conversions
Mechanical power is the rate at which work is done by forces or torques in motion (P = F·v or P = τ·ω). Electrical power is the rate at which electrical energy is transferred in a circuit (P = V·I). While both are measured in watts, they describe energy transfer in different physical systems. Motors convert electrical power to mechanical power, with efficiency determining how much is usefully transferred.
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