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Heat Pump COP Calculator

Find a heat pump's best-case COP.

Result

10.27
9.27

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.

Try this example →

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. Enter the hot and cold reservoir temperatures to find the ideal COP.

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