Heat pump COP and running cost calculator
A heat pump moves heat rather than making it, so it can deliver three or four units of heat per unit of electricity.
kWh
per kWh
per kWh
%
Annual heat pump running cost
1050.00
- Electricity used
- 3750 kWh
- Gas boiler cost for the same heat
- 954.55
- Annual saving
- -95.45
- Carnot ceiling COP
- 7.954
- Share of the Carnot limit achieved
- 40.2 %
- COP needed to match gas
- 3.520
Show the working
- Annual heat demand = 12 000
- Seasonal COP = 3.2
- Electricity price = 0.28
- Gas price = 0.07
- Boiler efficiency = 88
- Flow temperature = 45
- Source temperature = 5
- Electricity used = 12 000 / 3.2 = 3750
- Annual heat pump running cost = 3750 * 0.28 = 1050
- gas_used = 12 000 / (88/100) = 13 636.4
- Gas boiler cost for the same heat = 13 636.4 * 0.07 = 954.545
- Annual saving = 954.545 - 1050 = -95.4545
- Carnot ceiling COP = (45 + 273.15) - (5 + 273.15) > 0 ? (45 + 273.15) / ((45 + 273.15) - (5 + 273.15)) : 0 = 7.953 75
- Share of the Carnot limit achieved = 7.953 75 > 0 ? 3.2 / 7.953 75 * 100 : 0 = 40.2326
- COP needed to match gas = 0.07 > 0 ? 0.28 * (88/100) / 0.07 : 0 = 3.52
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- electricity = heat demand / COP
- Carnot COP = hot temperature in kelvin / temperature lift
- break-even COP = electricity price x boiler efficiency / gas price
Real heat pumps reach 40 to 55% of the Carnot ceiling. Anything claiming much more is measuring something else.
Every degree you can drop the flow temperature is worth roughly 2 to 2.5% on the COP, which is why radiator sizing matters so much.