Efficiency: output power and input power

Input power, useful power, losses

An engine (internal combustion, electric, etc.) receives energy in a particular form (electrical, chemical, etc.): this is the input power, denoted by P_a. It returns part of this in the form of useful mechanical work: this is the useful power, denoted by P_u. The remainder is lost, mainly in the form of heat (friction, Joule effect, etc.): P_lost = P_a - P_u.

Efficiency

The efficiency (eta, the Greek letter eta) of a system measures the effectiveness of this conversion:

eta = P_u / P_a

Efficiency is a dimensionless number, always between 0 and 1 (or expressed as a percentage). An efficiency of 1 (100%) is physically impossible for a real machine: there are always losses.

System	Typical efficiency
Electric motor	80–95%
Internal combustion engine (petrol)	25–35%
Incandescent light bulb	approximately 5%
Solar panel	15–22%

Example

An electric motor absorbs P_a = 500 W and delivers P_u = 400 W.

eta = 400/500 = 0.8, or 80 per cent.

Common pitfall

Do not confuse the direction of the fraction: efficiency is always useful power (what is recovered) divided by absorbed power (what is supplied to the system), never the other way round. An efficiency greater than 1 (100%) always indicates a calculation error.