Machine Efficiency

\eta = \frac{W_{out}}{W_{in}}

η =

Wout =

Win =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

No machine returns everything you put in: friction, elastic hysteresis, windage and noise take a cut, so η = W_out ⁄ W_in always lands below 1. Feed a hoist 1000 J and get 750 J of lifting done and it is 75% efficient, with 250 J warming the bearings. Enter η as a plain ratio or switch the unit to % — the calculator handles both.

The historical spread is enormous. Thomas Newcomen's 1712 atmospheric engine converted well under 1% of its coal's energy into work; Watt's separate condenser roughly tripled that; a modern combined-cycle gas turbine reaches about 60%, a large electric motor 95%, and a bicycle drivetrain around 97%. Efficiency chains multiply, which is why a 90%-efficient gearbox behind a 90%-efficient motor delivers 81% overall — and why the honest way to quote a system is end to end, not stage by stage.

Machine Efficiency

\eta = \frac{W_{out}}{W_{in}}

Where

$\eta$ = Efficiency
$W_{out}$ = Useful work output
$W_{in}$ = Work input

Missing one of these? Work it out first, then come back

Efficiency — Thermal Efficiency, Carnot Efficiency
Useful work output — Thermal Efficiency, Work (W = Fd cos θ)
Work input — Work (W = Fd cos θ), Power (P = W/t)

Part of this formula set

Work, energy and power

8 formulasWork, the two stores of mechanical energy, the theorem that connects them to speed, and the two ways of writing power.