What is Efficiency?
Efficiency is the ratio of useful energy output to total energy input, expressed as a percentage. No real system is 100% efficient — the gap is always waste heat, friction, or electromagnetic losses.
Universal Formula
η = (P_out / P_in) × 100%
= (Useful output / Total input) × 100%
Energy form: η = E_useful / E_input × 100%Worked Examples
Electric motor: 5 kW input, 4.3 kW shaft output
η = 4.3/5 × 100 = 86%
Gas furnace: 100,000 BTU/h input, 80,000 BTU/h heat output
η = 80% (AFUE rating)
Solar panel: 1000 W/m² sunlight, 200 W/m² electrical output
η = 20%Cascade Efficiency (Multiple Stages)
η_total = η₁ × η₂ × η₃ × ...
Gearbox (97%) × Motor (90%) × VFD (95%):
η = 0.97 × 0.90 × 0.95 = 0.830 = 83%Typical Efficiency Values
- LED light: 40-50% (vs incandescent 5%)
- Electric vehicle motor: 85-95%
- Steam turbine (power plant): 30-45%
- Natural gas combined cycle: 55-60%
- Human muscle: ~25%
Calculate system efficiency: Free Efficiency Calculator
Efficiency Formula
η = (useful output / total input) × 100%. For machines: η = P_out / P_in. For heat engines: maximum theoretical efficiency (Carnot) = 1 - T_cold/T_hot (temperatures in Kelvin). A steam turbine with steam at 500°C (773 K) exhausting at 50°C (323 K): Carnot η = 1 - 323/773 = 58.2% — no real turbine exceeds this. Actual modern steam turbines achieve 40–45%; combined-cycle gas turbines 60–62%. Electric motors: 90–98%. Transformers: 97–99.5%.
Efficiency by Technology
- Incandescent bulb: ~5% (light output vs electrical input)
- LED bulb: ~40–50% (significant improvement over incandescent)
- Solar PV (silicon): 15–23% (commercial panels)
- Petrol engine: 25–35% thermal efficiency
- Diesel engine: 35–45% thermal efficiency
- Fuel cell: 40–60% (direct electrochemical conversion)
- Electric motor: 90–98%
Frequently Asked Questions
Can efficiency exceed 100%?
For energy conversion devices (engines, motors, generators), no — conservation of energy prevents more useful output than total input. However, heat pumps appear to exceed 100% efficiency: they move 3–5 kWh of heat for every 1 kWh of electrical input (COP 3–5). This is not a violation of thermodynamics — the "extra" energy comes from the environment (ambient air, ground). The correct term for heat pumps is COP (Coefficient of Performance), not efficiency.
What is the efficiency of cascaded systems?
For systems in series, total efficiency = η₁ × η₂ × η₃ × ... An electric motor (η=0.92) driving a gearbox (η=0.96) connected by a belt drive (η=0.95) to a pump (η=0.75): overall η = 0.92 × 0.96 × 0.95 × 0.75 = 62.9%. Even moderate losses cascade — this motivates direct-drive and high-efficiency components throughout mechanical systems.
What is first-law vs second-law efficiency?
First-law efficiency compares actual useful output to total energy input. Second-law (exergy) efficiency compares actual performance to the thermodynamically ideal maximum (Carnot). A boiler may have 90% first-law efficiency (90% of fuel energy reaches the water) but only 30% second-law efficiency (only 30% of the maximum theoretical useful work is realised), because low-grade heat at 80°C has far less work potential than high-temperature combustion products.