Coefficient of Performance Calculator
Calculates the Coefficient of Performance (COP) for heat pumps and refrigerators. Use it to evaluate how efficiently a heating or cooling device converts electrical work into heat transfer.
About this calculator
The Coefficient of Performance (COP) is a dimensionless efficiency ratio that describes how much useful heat transfer a device delivers per unit of work consumed. For a heat pump (heating mode): COP_HP = Q_H / W, where Q_H is heat delivered to the hot reservoir. For a refrigerator or cooling device: COP_ref = Q_C / W, where Q_C is heat removed from the cold space. In both cases W is the work (or power) input. A COP greater than 1 is normal and expected — a heat pump with COP = 3 delivers 3 J of heat for every 1 J of electricity. The theoretical maximum COP is set by the Carnot limit: COP_Carnot = T_H / (T_H − T_C) for heating and T_C / (T_H − T_C) for cooling, where temperatures are in Kelvin.
How to use
Suppose a heat pump delivers 9,000 W of heat to a building while consuming 3,000 W of electrical power. Step 1 – identify inputs: Q_H = 9,000 W, W = 3,000 W, device type = heat pump. Step 2 – apply the formula: COP = Q_H / W = 9,000 / 3,000 = 3.0. This means the heat pump delivers 3 units of thermal energy for every 1 unit of electricity consumed. A COP of 3.0 is typical for a modern air-source heat pump in mild outdoor conditions.
Frequently asked questions
What is a good COP value for a heat pump or refrigerator?
For heat pumps operating in heating mode, a COP between 2.5 and 4.5 is considered good, with higher values achievable in mild climates. For refrigerators, a COP of 2 to 6 is typical, depending on the temperature difference between the interior and the room. The closer the two temperature reservoirs are to each other, the higher the achievable COP. Real-world devices always fall below the theoretical Carnot maximum due to irreversibilities like friction and heat leakage.
How is the COP of a refrigerator different from the COP of a heat pump?
For a refrigerator, COP is defined as the heat removed from the cold space (Q_C) divided by the work input, measuring cooling effectiveness. For a heat pump in heating mode, COP is the heat delivered to the warm space (Q_H) divided by work input. Because Q_H = Q_C + W by energy conservation, the heat pump COP is always exactly 1 greater than the refrigerator COP for the same operating conditions. Selecting the correct device type in the calculator ensures you get the right interpretation of the result.
Why can the coefficient of performance be greater than 1 unlike ordinary efficiency?
Ordinary efficiency compares useful output energy to input energy for the same energy form, so it cannot exceed 1 (100%). COP, however, compares heat transferred — which is moved, not generated — to the work consumed. A heat pump moves thermal energy from a cold reservoir to a hot one, so the total heat delivered can far exceed the electrical energy used to run the compressor. This is why COPs of 3 or 4 are physically valid and desirable; they do not violate energy conservation because the extra energy comes from the environment.