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Heat Pump COP Calculator

Find a heat pump's best-case COP.

How it is calculated

The tool gives the ideal (Carnot) coefficient of performance, the theoretical ceiling for any heat pump between two temperatures. Both temperatures are entered in °C and converted to kelvin by adding 273.15: Th = hot + 273.15, Tc = cold + 273.15. Then COPheating = Th ÷ (Th − Tc) and COPcooling = Tc ÷ (Th − Tc). The hot side must be warmer than the cold side, otherwise there is no result. Real machines reach only a fraction of this figure because of compressor losses, defrost cycles and fan power.

Worked example

A heat pump delivers 35 °C water (floor heating) from outside air at 5 °C. In kelvin: Th = 308.15 and Tc = 278.15, so the difference is 30. Heating: 308.15 ÷ 30 = 10.27. Cooling: 278.15 ÷ 30 = 9.27. In theory each unit of electricity could move about 10 units of heat; a real unit will give noticeably less.

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Common mistakes

  • Typing temperatures in kelvin or °F. The fields expect °C and the conversion is done for you.
  • Expecting the result to match the datasheet COP. This is the theoretical maximum; measured seasonal values are much lower.
  • Using the room temperature as the hot side for a water-heated system. Use the supply temperature the heat pump actually delivers.
  • Swapping hot and cold. If the "hot" value is not higher, the tool returns nothing.
  • Ignoring that a smaller temperature difference gives a much higher COP, which is why low-temperature floor heating suits heat pumps.

About this calculator

The coefficient of performance (COP) of a heat pump measures how much heat energy it moves per unit of electrical energy consumed — a COP of 4 means 4 units of heat delivered for every 1 unit of electricity used. The ideal, theoretical maximum is the Carnot COP, set by thermodynamics alone: for heating, COP_heating = T_hot / (T_hot − T_cold), and for cooling, COP_cooling = T_cold / (T_hot − T_cold), with both temperatures in Kelvin — no real machine can exceed this limit.

HVAC engineers and energy analysts use the Carnot COP as a theoretical benchmark against which real heat pump efficiency is measured (real units typically achieve 40–60% of the Carnot value), and it explains why heat pumps become less efficient in very cold climates — as the outdoor-indoor temperature gap widens, the Carnot ceiling drops, so there's less heat to extract per unit of work.

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Comments (1)

  • Editorial team

    These figures are the theoretical Carnot limit for the two temperatures you enter, in degrees Celsius, so a real machine will always come in below them. What the numbers teach well is the direction: a smaller gap between source and delivery temperature gives a higher COP, which is why low-temperature floor heating suits a heat pump better than hot radiators. Compare any claimed seasonal figure against this ceiling. What supply temperature does your system run at?

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