How this instrument works
Efficiency is a ratio wearing a percent sign: divide what the machine delivers in the form you actually wanted by everything you fed it, and out comes η (eta), a pure number between zero and one. Joules cancel joules, so η carries no unit at all — its SI dimension is 1, and percent is merely shorthand for hundredths. Whatever fraction goes missing has not vanished. Energy is conserved; it simply left as heat, sound, vibration, or light nobody asked for.
Sadi Carnot put a ceiling on this whole business in 1824. Reflecting on steam engines around him — Newcomen's early machines turned barely half a percent of their coal into work, Watt's improved designs a few percent — he proved that no heat engine can beat 1 − Tc/Th, the limit set purely by absolute temperatures between which it runs. That is why modern combined-cycle gas turbines stall near 64% instead of climbing toward 100: thermodynamics, not sloppy engineering, holds that line.
This ratio only means something once you fix the boundary and decide what counts as useful. Rate a petrol engine at its crankshaft and you get roughly 30%; count refining and drilling too, and well-to-wheel figures fall below 20%. Rate a power station on electricity alone and it scores 40%, but pipe its waste heat into nearby homes and that same plant reports 80%. Move the fence, move the number — which is why any honest efficiency quote names its system first.
- Enter delivered output into Useful energy out — joules, kilojoules, watt-hours, or food calories are all accepted.
- Enter total supplied into Energy in, using whatever unit your meter or fuel table reports; mixing units across the two fields is fine, since conversion happens before division.
- Read Efficiency (%) — that ratio already multiplied by 100 and carried to three figures.
- If the sheet warns that useful output cannot exceed energy supplied, check your boundary: some input has almost certainly gone uncounted.
Worked example — a sticky block and tackle
A workshop hoist rigged as a two-fall tackle should lift 50 newtons — about 5.1 kg — for roughly 25 N of pull. This one is old, its sheaves dry and its rope stiff, so it demands the full 50 N. Hauling 2 metres of rope through your hands does 50 × 2 = 100 J of work; the load rises 1 metre, banking 50 × 1 = 50 J. Enter 50 J into Useful energy out and 100 J into Energy in, and Efficiency (%) reads 50.
Those missing 50 joules went into friction at sheave pins and into bending stiff rope around each turn; haul long enough and you can feel warmth in your palms. Grease those pins so pull drops to 30 N, and work in falls to 60 J while output holds at 50 J — efficiency climbs to 83%. Nothing about that load changed. Only losses did.
Questions
Can efficiency ever exceed 100%?
Not for an energy conversion — that would create energy from nothing. Heat pumps and refrigerators do post figures above 100%, but they move heat rather than making it: one joule of electricity can shift four joules of warmth indoors from cold outside air. Engineers avoid confusion by rating those machines with a coefficient of performance instead, and this sheet rejects any output larger than its input for exactly that reason.
What unit does efficiency have?
None at all. Joules divided by joules cancel, leaving a pure number whose coherent SI unit is 1. Percent is not a unit either — NIST SP 811 treats the symbol % as shorthand for the factor 0.01, which is why 0.5 and 50% say an identical thing. Only one discipline matters here: both energies must be expressed in matching units before you divide.
How do I combine efficiencies across several stages?
Multiply them, never average them. A 90% gearbox driven by a 40% engine delivers 0.90 × 0.40 = 36% overall, not 65%. Losses compound, so one weak stage dominates an entire drivetrain — which is why designers hunt for their worst link rather than polishing an already good one. Convert each percentage to a decimal, multiply, then scale back by 100.
Why can't a heat engine reach 100%?
Because the second law forbids it. Carnot showed that an engine drawing heat at absolute temperature Th and rejecting it at Tc is capped at 1 − Tc/Th, however perfect its parts. Steam at 850 K exhausting to 300 K therefore tops out near 65%, and friction, leakage, and pumping losses claim another slice. Machines that never route energy through heat — motors, generators, transformers — climb into high nineties instead.
Can I put power in these fields instead of energy?
Only after converting, since both fields are typed in energy units running from joules to kilowatt-hours. Multiply a steady power by its running time: a 60 W lamp burning for 3600 s draws 216 kJ. Ratios of steady powers equal ratios of energies anyway, because that shared second cancels; what wrecks an answer is mismatched timing, such as output over one hour against input measured across a whole day.
What actually counts as useful energy out?
Whatever your application wants, which makes it an engineering decision rather than a measurement. Waste heat from a generator is worthless to a grid operator and valuable to a district heating scheme, so one identical plant scores 40% or 80% depending on who asks. State your intended output before quoting any number, and treat any efficiency claim with no stated boundary as marketing.