Heat Pump COP & Running Cost Calculator

Understanding the heat pump COP and running cost calculator — concept and principle

A heat pump's coefficient of performance (COP) tells you how many units of heat it delivers for each unit of electricity it uses. This calculator turns a heating demand into electricity use and running cost, and compares it with a gas boiler supplying the same heat.

With COP 3.2, each kWh of electricity delivers 3.2 kWh of heat — about 12% cheaper than gas here.

How it is calculated

Electricity used: E = Q / COP
Heat pump cost: E × electricity price
Gas boiler cost: Q / (boiler efficiency / 100) × gas price

Q is the heat delivered to the home in kWh. COP is dimensionless; for a yearly estimate use the seasonal value (SCOP), which averages over changing outdoor temperatures. Prices are per kWh in any currency, as long as both use the same one.

The principle

A heat pump does not burn fuel to make heat; it uses electricity to move heat that already exists in outdoor air, ground or water up to a higher temperature. That is why one kWh of electricity can deliver three or more kWh of heat. A boiler can only convert the fuel's energy into heat, minus flue and other losses, so its efficiency stays below 100%. The comparison therefore comes down to one ratio: the heat pump is cheaper when electricity price ÷ COP is lower than gas price ÷ boiler efficiency.

Worked example

Inputs: Q = 1000 kWh, COP = 3.2, electricity 0.25 per kWh, gas 0.08 per kWh, boiler efficiency 90%.
Electricity used: 1000 / 3.2 = 312.5 kWh.
Heat pump cost: 312.5 × 0.25 = 78.125.
Gas needed: 1000 / 0.90 = 1111.11 kWh; gas cost: 1111.11 × 0.08 = 88.88888889.
Check with the ratio: 0.25 / 0.08 = 3.125, which is below 3.2 / 0.90 = 3.56, so the heat pump is cheaper, by about 12%.

Each point is the calculator re-run with only “COP / SCOP” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

COP / SCOP	Electricity used (kWh)
0.8	1,250
1.6	625
2.4	416.6666667
3.2	312.5
4	250
4.8	208.3333333
6.4	156.25

How to read the result

The COP falls as the temperature lift grows, so a heat pump is most efficient with mild outdoor air and low flow temperatures such as underfloor heating or large radiators. In very cold spells or with high flow temperatures the instantaneous COP can drop well below its rated value. Small changes in the price ratio can flip the comparison, so it is worth recalculating with your actual tariffs and the SCOP of the specific unit.

Common mistakes

Using the best-case COP from a brochure (measured at mild conditions) for a whole winter.
Entering the heat pump's electrical input as Q; Q must be the heat delivered.
Forgetting standing charges, maintenance, and that gas may be billed on a different calorific basis.

Keep in mind: This is a simplified energy-cost estimate, not financial advice. Real costs depend on tariffs, installation quality, building insulation, controls and climate. Get a heat-loss survey and quotes from a qualified installer before investing.

Frequently asked questions

What is the difference between COP and SCOP?

COP is measured at one set of conditions; SCOP is a seasonal average over a heating season and is the better figure for annual costs.

How do I know how much heat my home needs?

Use past gas consumption multiplied by the old boiler's efficiency, or a professional heat-loss calculation.

Sources: EN 14825, Air conditioners, liquid chilling packages and heat pumps — Testing and rating at part load conditions and calculation of seasonal performance · Y. A. Çengel and M. A. Boles, Thermodynamics: An Engineering Approach, McGraw-Hill

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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