COP is the multiplier that makes heat pumps interesting: delivered thermal output divided by electrical input, so electrical power = load ÷ COP. Its ceiling is thermodynamic — the Carnot COP, a ratio of absolute temperatures: Th/(Th − Tc) for heating and Tc/(Th − Tc) for cooling, which is why both temperatures must be in kelvin (Celsius in that formula gives wrong, often negative, answers). Real vapour-compression machines reach roughly 40–55% of the Carnot limit once compressor, motor, and heat-exchanger losses are paid, so actual COP = η_carnot × COP_carnot with η around 0.45–0.50.
A worked lift shows the scale: an air-source heat pump moving heat from 0 °C outdoor air to a 35 °C underfloor flow spans 35 K, giving a Carnot heating COP of 308.15/35 = 8.80 and, at η = 0.50, an actual COP of 4.40. Meeting a 10 kW load then draws 10/4.40 = 2.27 kW; over 1,000 hours at 0.30 per kWh that is about 681, against 3,000 for electric resistance heating at COP = 1 — a saving of roughly 77%, which is exactly 1 − 1/COP.
Two identities knit the ratings together: COP_heating = COP_cooling + 1 for the same reservoirs (the condenser delivers the absorbed heat plus the compressor work), and EER = COP × 3.412 converts to the BTU-per-watt-hour convention of AHRI 210/240 ratings, with EN 14825 defining the seasonal SCOP/SEER counterparts. The catch is weather: as the source gets colder the lift grows and COP falls, and below a balance point the system leans on supplementary resistance heat — sharply raising the running cost the COP had been suppressing.