Boneyard Tools

COP for refrigerators and heat pumps explained

How coefficient of performance measures cooling and heating machines, why it exceeds one, and how it links to the Carnot limit and to EER.

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Moving heat is not the same as making heat

An electric heater turns work straight into heat, so at best it returns one joule of heat per joule of electricity. A refrigerator or heat pump does something cleverer: it uses work to pump heat from one place to another. Because it moves heat that is already present in the cold reservoir instead of creating it, the useful energy delivered can be several times the work spent. That is why the coefficient of performance is written as heat moved over work, and why it routinely lands above one.

Two modes, one ratio

The same hardware can be described two ways depending on what you want from it. Run it as a refrigerator and the useful output is Qc, the heat pulled out of the cold space, giving the cooling COP. Run it as a heat pump and the useful output is Qh, the heat dumped into the warm space, giving the heating COP. Energy conservation ties them together: the heat rejected equals the heat absorbed plus the work added, so Qh = Qc + W, and the heating COP is always exactly one more than the cooling COP for the same cycle.

The Carnot ceiling

No real machine can beat the reversible Carnot limit set by the two temperatures it works between, measured in kelvin. For cooling the ceiling is Tc divided by (Th minus Tc); for heating it is Th divided by (Th minus Tc). The lesson is practical: the smaller the temperature gap a unit has to bridge, the higher its possible COP. This is why heat pumps lose efficiency on very cold days and why geothermal loops, which face a milder ground temperature, outperform air-source units.

COP, EER and the numbers on a label

Equipment in the United States is often rated in EER or SEER rather than COP, but they measure the same idea in different units. EER divides cooling capacity in BTU per hour by power draw in watts, so multiplying an EER by about 0.293 converts it to a dimensionless cooling COP, and dividing a COP by that factor goes the other way. SEER averages performance across a season of conditions, so it usually reads higher than a single-point EER. Converting a spec sheet into COP with this calculator lets you compare machines on one honest scale.

Frequently asked questions

Can COP be less than 1?

Yes, though it is unusual for a well-matched system. If the work input approaches the heat moved, for example a struggling unit bridging a huge temperature gap, the ratio can fall toward or below 1. At that point simple resistive heating may be just as efficient.

How do I convert an EER rating to COP?

Multiply the EER by about 0.293 to get the dimensionless cooling COP, since 1 watt equals roughly 3.412 BTU per hour. For example an EER of 12 corresponds to a cooling COP near 3.5.

Why does a heat pump's COP drop in winter?

COP falls as the gap between indoor and outdoor temperature grows. On a cold day the unit must lift heat across a larger temperature difference, which the Carnot limit penalizes, so both the ideal and the real COP decline.