Heat Pump COP Calculator
A heat pump's coefficient of performance (COP) tells you how much heat it delivers per unit of electricity. Because it moves heat rather than generating it, a good heat pump delivers several units of heat per unit of power, which is why it can be far more efficient than direct electric heating. This calculator works out the COP from your heat output and electrical input, then compares it against the Carnot limit set by the hot and cold temperatures. Enter measured values for a real figure; the Carnot comparison shows how close to the thermodynamic ceiling the unit runs.
Heat pump COP formula
COP = heat output / electrical input
T_hot (K) = hot Celsius + 273.15
T_cold (K) = cold Celsius + 273.15
Carnot COP = T_hot / (T_hot - T_cold)
Carnot efficiency = COP / Carnot COP * 100
Heat from environment = COP - 1
Heat from environment (COP minus 1) is the free heat moved per unit of electricity: the rest of the delivered heat comes from the power input. The Carnot efficiency shows how close the real unit gets to the ideal.
What raises COP
- A smaller temperature lift (mild outdoor air, lower flow temperature) raises both real and Carnot COP.
- Low-temperature heat distribution (underfloor, large radiators) lets the pump run at a lower hot-side temperature.
- Good defrost behaviour and correct sizing keep real COP near its design point.
- Compare your measured seasonal figure, not just the nameplate, for honest efficiency.
Heat pump COP: frequently asked questions
What is the coefficient of performance (COP)?
COP is the ratio of useful heat delivered to the electrical energy consumed: COP = heat output / electrical input. A COP of 3 means the heat pump delivers three units of heat for every unit of electricity, by moving heat from outside rather than generating it. A higher COP means a more efficient heat pump.
What is the Carnot COP limit?
The Carnot COP is the theoretical maximum for heating between two temperatures: hot temperature divided by the temperature difference, both in kelvin. Carnot COP = T_hot / (T_hot - T_cold). Real heat pumps reach a fraction of this ideal; comparing your measured COP to the Carnot limit shows how close to the thermodynamic ceiling the unit operates.
Why convert temperatures to kelvin?
The Carnot formula is a ratio of absolute temperatures, so both must be in kelvin (Celsius plus 273.15). Using Celsius directly would give a meaningless result. This calculator converts the temperatures you enter in Celsius to kelvin for the Carnot limit.
What is a typical heat pump COP?
It depends on the technology and the temperature lift: smaller lifts (mild outdoor temperatures, low flow temperatures) give higher COP. Air-source units often operate with seasonal COPs in the low single digits, while ground-source units can be higher. Enter your own measured heat output and electrical input for a real figure.
Official sources
- U.S. Department of Energy: Heat Pump Systems.
- U.S. Department of Energy, Office of Energy Efficiency: Heating and Cooling.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.