Formula & Calculator
Electrical Efficiency
Expresses how much of the input power is converted into useful output power.
Interpretation
Electrical efficiency η is the ratio of output power to input power, multiplied by 100% to get a percentage.
It indicates how much of the input energy is converted to useful work.
Example: P_in=200W, P_out=170W → η = (170/200)×100 = 85%.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| η | Electrical efficiency | % (or dimensionless) |
| P_out | Output power (useful power delivered) | W, kW, or MW |
| P_in | Input power (total power supplied) | W, kW, or MW |
What it means
Electrical efficiency η is the ratio of output power to input power, often expressed as a percentage. η = (P_out / P_in) * 100%. It measures how effectively a device converts input electrical energy into useful output (e.g., mechanical, thermal, or another electrical form). Losses are due to heat, friction, and other inefficiencies. Efficiency is a critical specification for motors, generators, transformers, power supplies, and lighting. Higher efficiency means less wasted energy, lower operating costs, and reduced environmental impact. Efficiency is often used to compare different products or to determine the payback period for energy‑efficient upgrades. Example: If a motor draws 200W of electrical power and delivers 170W of mechanical power, its efficiency is (170/200)*100 = 85%. The remaining 15% is lost as heat.
Worked example
Electrical Efficiency – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Pin | 1.5 kW |
| Pout | 1.2 kW |
| Formula | η = (Pout / Pin) × 100% |
Common mistakes
- Output/Input: Use the same units for both (watts).
- Losses: Efficiency = 1 − (losses/input).
- Maximum efficiency: Occurs when copper losses equal iron losses (for transformers).
- Percentage: Multiply by 100 to get a percentage.
- Nameplate: Efficiency is often given at full load.
Applications
Electrical efficiency η is the ratio of output power to input power, expressed as a percentage. It measures how much of the input energy is converted into useful work, with the rest dissipated as heat. Engineers use efficiency to select motors, transformers, and power supplies, to reduce operating costs, and to meet regulatory standards. High‑efficiency appliances save energy and reduce environmental impact. By calculating efficiency, professionals can compare different devices and justify investments in more efficient equipment. This formula is central to energy management and sustainability. Understanding efficiency helps in making informed decisions in both design and operation.
- Motor and generator efficiency evaluation
- Power supply and converter efficiency design
- Energy audits and efficiency improvement projects
- Compliance with energy efficiency standards
- Educational understanding of energy conversion losses
Frequently Asked Questions
Efficiency is η = (P_out / P_in) × 100%, the ratio of output power to input power.
Small motors: 50-80%; large industrial motors: 90-97%; premium efficiency motors can exceed 95%.
Copper losses (I²R), core losses (eddy current and hysteresis), mechanical losses (friction), and stray losses.
Losses = P_in − P_out = P_in (1 − η).
Efficiency is the ratio of output to input power; power factor is the ratio of real to apparent power.
Efficiency is usually highest near full load; at very low loads, fixed losses dominate and efficiency drops.
Savings = (P_in_old − P_in_new) × operating hours × energy cost.
IE1 (Standard), IE2 (High), IE3 (Premium), IE4 (Super Premium), based on IEC standards.
By measuring input power (with a wattmeter) and output power (mechanical torque and speed for motors), or using a calorimetric method.
Common errors include: 1) using the wrong units, 2) forgetting to include all losses, 3) using peak instead of average power, 4) confusing efficiency with power factor, and 5) applying to non-linear loads without proper measurement.