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Coefficient of Performance (COP)

Also known as COP

COP=Q˙W˙\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}
sig figs

Worked example: 12 kW delivered on 3 kW input → COP 4.0. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Coefficient of Performance (COP) fits

Your answer feeds
EER to COP Conversion
In this toolkit

See also

EER to COP Conversion: Both use coefficient of performance.Refrigeration COP from Enthalpies: Both use coefficient of performance.Chiller Efficiency (kW per Ton): Both use power input.Energy Efficiency Ratio (EER): Both use power input.Heat Rejected by a Power Plant (from the Electric Output and the Thermal Efficiency): Both use power input.
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Tons, EER and COP →

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Coefficient of Performance (COP) explained

COPWQ

A heat pump does not make heat, it moves it, which is why a COP above 1 is not a violation of anything: a COP of 4 means every kilowatt of electricity shoves four kilowatts of heat across the wall. Electric resistance sits stubbornly at COP 1.0; a modern air-source heat pump manages 3.5–4.5 at 8 °C outdoors and perhaps 2.0 at −15 °C; a ground-source loop sitting in stable 10 °C earth holds 4–5 all winter, which is exactly why geothermal contractors care so much about loop flow and antifreeze concentration.

The ceiling is Carnot: COPmax = Thot/(Thot − Tcold) in kelvin, so a machine lifting heat from 0 °C to 40 °C can never beat 313/40 ≈ 7.8, and real equipment lands at 40–55 % of that. The trap in cold climates is the auxiliary heat strip: a 3 kW resistance element energised alongside the compressor drags the system COP down fast, so the sticker COP and the winter bill tell different stories. Worked example: a unit delivering 12 kW while drawing 3 kW has COP = 12/3 = 4.0, equivalently EER 13.6 or 400 % efficiency in the marketing brochure.

Coefficient of Performance (COP) formula

COP=Q˙W˙\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}
Where
  • COP\mathrm{COP}= Coefficient of performance
  • Q˙\dot{Q}= Heating or cooling delivered (W)
  • W˙\dot{W}= Power input (W)
In this toolkit

Refrigeration capacity and efficiency

6 formulasTons, COP, EER and kW per ton — the four ways the trade states the same chiller performance, and how to convert between them.

Revised 31 October 2026
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formula.expert. (2026, October 31). Coefficient of Performance (COP) Formula & Calculator. https://formula.expert/solvers/coefficient-of-performance

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