Refrigeration Cycle COP

Coefficient of performance for a cooling or heating cycle from duty and compressor power, with the Carnot ceiling for comparison.

InputCOP_cool = Q_c / W , COP_heat = (Q_c + W) / W = COP_cool + 1 , COP_Carnot = T_c / (T_h − T_c)

Cooling duty (evaporator) (kW)or enter ton (refrig) — converts to kWCompressor power input (kW)or enter hp — converts to kWCold reservoir temp (evaporator) (°C) — optionalor enter °F — converts to °CHot reservoir temp (condenser) (°C) — optionalor enter °F — converts to °C

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The engineering

The coefficient of performance is useful cooling (or heating) divided by the work you paid for. For a refrigerator or chiller it is the evaporator duty over compressor power; for a heat pump in heating mode it is the condenser heat over compressor power, which is always exactly one greater than the cooling COP because the compressor work also ends up as heat.

Enter the reservoir temperatures to get the Carnot ceiling — the best any cycle between those two temperatures could ever do. Real vapor-compression chillers land at 40–60% of Carnot; a second-law efficiency above ~70% means you either have a very good machine or an optimistic spec sheet. Note EER quotes cooling in Btu/h per watt, so EER ≈ 3.412 × COP.

Sanity check: the tighter the temperature lift (T_h − T_c), the higher the COP — which is why raising chilled-water setpoint or lowering condenser temperature pays off so directly.

Where this math comes from

Sadi Carnot laid the groundwork in 1824 with Réflexions sur la puissance motrice du feu, proving that the maximum efficiency of any cycle depends only on the two temperatures between which it operates — the reversed version of that argument sets the ceiling on every refrigerator and heat pump ever built.

Practical mechanical refrigeration arrived with Jacob Perkins' 1834 vapor-compression patent and matured through Carl von Linde's industrial ammonia machines in the 1870s. The COP metric became the common bench language of the refrigeration trade, and ASHRAE now standardizes how duty, power, and rating conditions are measured and reported.

1824Sadi CarnotEstablishes the temperature-only limit on cycle efficiency — the Carnot COP.
1834Jacob PerkinsPatents a working vapor-compression refrigeration machine.
1876Carl von LindeBuilds practical ammonia refrigeration plants, launching industrial cooling.
2021ASHRAEHandbook — Fundamentals codifies COP/EER rating conditions and measurement.

See the full timeline of the math behind every calculator →

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