Coefficient of Performance (COP) Calculator
Calculate the COP of a heat pump, refrigerator or air conditioner from heat and power, compare it with the Carnot limit between the hot and cold temperatures, and get EER and tons of refrigeration.
How it works
Heat pump: COP_HP = Q_H / W, Carnot COP = T_H / (T_H − T_C) · Refrigerator / AC: COP_R = Q_C / W, Carnot COP = T_C / (T_H − T_C) · temperatures in kelvin · energy balance Q_H = Q_C + W · EER = 3.412 × COP_R
The coefficient of performance is the useful heat moved divided by the work put in. Because a heat pump moves heat rather than making it, its COP is normally above 1 — 3 means three units of heat for each unit of electricity. The second law of thermodynamics caps the COP at the Carnot value, which falls as the temperature lift between the cold and hot sides grows; real machines usually reach 40–60% of it. Definitions follow Çengel & Boles (Thermodynamics, ch. 6) and the US Department of Energy’s heat-pump guidance.
Worked example
A heat pump delivers 10 kW of heat while drawing 3 kW of electricity: COP = 10 / 3 = 3.33. Between 5 °C outside (278.15 K) and a 35 °C supply (308.15 K) the Carnot COP is 308.15 / 30 = 10.27, so the second-law efficiency is 32.5%. The other 7 kW is absorbed from the outdoor air, and every kWh of electricity yields 3.33 kWh of heat.
Sources: Çengel & Boles — Thermodynamics: An Engineering Approach, Ch. 6 (refrigerators and heat pumps) · US Department of Energy — Heat Pump Systems
Frequently asked questions
What is a good COP for a heat pump?
Modern air-source heat pumps reach a COP of about 3–4 in mild weather and 2–2.5 near −10 °C; ground-source units manage 4–5. The seasonal average (SCOP or HSPF) is the best guide to running costs.
Why is COP for heating 1 higher than for cooling?
For the same cycle Q_H = Q_C + W, so COP_HP = COP_R + 1. The work input ends up as heat on the hot side, which is useful for heating but not for cooling.
What is the difference between COP and EER?
They measure the same thing in different units. EER is BTU/h of cooling per watt of electricity, so EER = 3.412 × COP. SEER averages EER over a cooling season.
Why does COP drop in cold weather?
The heat pump must lift heat across a bigger temperature difference. The Carnot COP T_H/(T_H − T_C) falls as T_C drops, and the real COP follows.
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Results assume the idealised textbook model stated above; real systems have losses and tolerances, so verify safety-critical values with measurements or a qualified engineer.