Coefficient of Performance (COP)

Also known as COP

\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}

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

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Tons, EER and COP →

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Coefficient of Performance (COP) explained

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: COP_max = T_hot/(T_hot − T_cold) 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

\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}

Where

$\mathrm{COP}$ = Coefficient of performance
$\dot{Q}$ = Heating or cooling delivered (W)
$\dot{W}$ = Power input (W)

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

Coefficient of performance — EER to COP Conversion, Refrigeration COP from Enthalpies
Heating or cooling delivered — Tons of Refrigeration from BTU/hr, Energy Efficiency Ratio (EER)
Power input — Energy Efficiency Ratio (EER), Chiller Efficiency (kW per Ton)

Part of this formula set

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.