Heat pump coefficient of performance:
formula and worked example

What COP says about a heat pump

A resistance heater turns each unit of electricity into one unit of heat. A heat pump uses electricity to move heat from a cold source, such as outside air, to a warm space, so it can deliver more heat than the electrical energy it uses. The coefficient of performance puts a single number on that ratio.

COP is the main efficiency measure for comparing heat pumps with each other and with electric heaters. A higher figure means lower running cost for the same heat delivered, at the same tariff.

It is a point value, measured at a specified condition. Real operation covers a range of conditions, so a single COP describes one moment rather than a whole winter.

The formula and what goes in

• Heat output in kW is the thermal power delivered to the heated space or water at the stated conditions.
• Electric input in kW is the electrical power the unit draws at the same moment, including the compressor and normally the fans and controls.
• The result has no unit, since kilowatts cancel; it is often written as a multiple.

If heat is given in BTU per hour or tonnes of refrigeration, convert it to kW first so that the ratio is meaningful.

Worked example: 10 kW out for 2.5 kW in

A heat pump is rated to deliver 10 kW of heat while drawing 2.5 kW of electricity at a given test condition.

1. 1Heat output: 10 kW.
2. 2Electric input: 2.5 kW.
3. 3Divide: 10 / 2.5 = 4.
4. 4Interpretation: each kilowatt-hour of electricity produces four kilowatt-hours of heat.

By comparison, a resistive heater delivering 10 kW would draw 10 kW, a COP of 1.

What a COP of 4 means

A COP of 4 means the system delivers four units of heat for each unit of electricity, so running it is one quarter of the cost of a resistance heater for the same output. In practice the cost advantage depends on the tariff and on how the COP behaves over the season.

COP falls as the temperature difference between the source and the delivery grows. A pump with a high figure at mild outdoor temperatures will show a lower one on very cold days or when delivering water at high temperatures, which is why seasonal figures exist.

• Always read the test conditions beside the COP, such as the outdoor and delivery temperatures.
• A seasonal figure is a better guide to annual running cost than a single-point COP.

What happens if heat output rises by 10%

Keeping the electrical input at 2.5 kW and raising the heat output from 10 to 11 kW lifts the COP from 4 to 4.4.

The table isolates one variable, which a real machine seldom does. Heat output and electric input usually move together when conditions change, so a well-designed comparison measures both at each condition.

Mistakes when reading COP figures

• Comparing COPs measured at different temperatures as if they were the same test.
• Treating a cooling-mode ratio, often called EER, as a heating COP when the machine is used for heating.
• Leaving out the fan or defrost power from the electric input, which makes the ratio look better than it is.
• Thinking a COP over 1 is impossible; it is only the heat being moved rather than created.

Check the datasheet to see whether the figure includes auxiliary power.

Using COP in a running cost estimate

To compare options, divide the heat you need by the COP to find the electricity required, then multiply by the tariff. A heat demand of 100 kWh at COP 4 needs 25 kWh of electricity; with a resistance heater it needs 100.

Keep delivery temperature as low as the building allows. Underfloor loops and large radiators let the heat pump work at a better COP than small, high-temperature emitters.