Calculate heating or cooling COP, useful output, or input power, then compare EER, energy balance, Carnot COP, and second-law efficiency.

Use positive magnitudes on the same time basis. The complementary heat balance assumes one heat-pump cycle with QH = QC + W and no additional losses.

This choice sets the meaning of both numbers; it does not convert them. Energy amounts must cover the same interval.

COP Formula

The following formula is used to calculate the coefficient of performance of a heat pump.

COP = | Q | / W
  • Where COP is the coefficient of performance
  • Q is useful heat delivered at the condenser in heating mode or removed at the evaporator in cooling mode (energy, such as kWh)
  • W is input work over the same interval (energy, such as kWh). Alternatively, use heat-transfer rate and input power in matching units such as kW.

Divide useful heat by input work, or useful heat-transfer rate by input power, using matching units and the same measurement boundary.

COP Definition

What is COP?

COP stands for coefficient of performance. This is a term used to describe the ratio of useful heat output or removal by a heat pump and the work or power supplied by the compressor to the heat pump.

Example Problem

How is COP calculated?

COP is calculated by dividing the absolute value of the total heat output or removal of a heat pump by the work or power supplied to the pump.

How to calculate COP?

  1. First, determine the work supplied to the heat pump over a stated interval.

    For this example, the input work over that interval is 20 kWh.

  2. Next, determine the useful output or removal of heat by the pump.

    In this case, the heat pump removes 30 kWh of heat.

  3. Finally, calculate COP.

    Using the formula above, the COP is calculated to be:
    COP = | Q | / W
    COP = 30 / 20
    COP = 1.5