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Machine Efficiency

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

Worked example: 750 J out of 1000 J → η = 0.75 — press Try an example to run it live, then adjust anything.

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Machine Efficiency explained

ηWinWout

No machine returns everything you put in: friction, elastic hysteresis, windage and noise take a cut, so η=Wout/Win\eta = W_{\text{out}} / W_{\text{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 formula

η=WoutWin\eta = \frac{W_{out}}{W_{in}}
Where
  • η\eta= Efficiency
  • WoutW_{out}= Useful work output (J)
  • WinW_{in}= Work input (J)

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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.