About Heat Pump COP Calculator
The heat pump COP calculator returns the ideal Carnot coefficient of performance and the realistic actual COP for a vapour-compression heat pump operating between a heat source and a delivery (sink) temperature. It works in both heating and cooling modes and reports the EER, the electrical input power needed to meet a building load, the delivered thermal output, the running electricity cost, and the money saved compared with simple electric resistance heating.
Enter the source and sink temperatures in degrees Celsius, a Carnot (second-law) efficiency between 0 and 1 (typically 0.4–0.5 for real machines) or a measured rated COP, the thermal load in kilowatts, the electricity price, and the operating hours. The tool converts temperatures to absolute kelvin, applies the Carnot relations, and plots how COP falls as the source gets colder so you can anticipate cold-weather performance and the balance point with a back-up heater.
How It Works
- Choose heating or cooling mode and enter the source (outdoor/ground/water) and sink (delivery/chilled) temperatures in °C.
- Provide either a Carnot efficiency (0–1, usually ~0.45) or a measured rated COP; the rated COP overrides the Carnot path.
- The calculator converts to kelvin and computes Carnot COP = Th/(Th−Tc) for heating or Tc/(Th−Tc) for cooling, then actual COP = η_carnot × Carnot COP.
- It derives EER = COP × 3.412, electrical input = load ÷ COP, running cost = input × hours × price, and savings versus resistance heating (COP = 1).
Worked Example
An air-source heat pump lifts heat from 0°C outdoor air (273.15 K) to a 35°C underfloor flow (308.15 K), a 35 K lift, with a Carnot efficiency of 0.50. The Carnot heating COP is 308.15 / 35 = 8.80; the actual COP is 0.50 × 8.80 = 4.40. To deliver a 10 kW load the heat pump draws 10 / 4.40 = 2.27 kW. Over 1000 hours at 0.30 per kWh it costs 2.27 × 1000 × 0.30 = 681. Resistance heating (COP = 1) would cost 10 × 1000 × 0.30 = 3000, so the heat pump saves about 2319, roughly 77% (= 1 − 1/4.40).
Formulas
- Carnot COP — heating
COP_carnot,heat = Th / (Th - Tc)- Carnot COP — cooling (EER ideal)
COP_carnot,cool = Tc / (Th - Tc)- Heating–cooling identity
COP_heating = COP_cooling + 1- Actual COP and EER
COP = eta_carnot * COP_carnot ; EER = COP * 3.412- Energy balance, cost and savings
input = load / COP ; cost = input * hours * price ; savings = (load - input) * hours * price
Standards & References
- Carnot’s theorem / second law of thermodynamics
- EN 14825 (seasonal space heating/cooling efficiency, SCOP/SEER)
- ASHRAE Handbook — HVAC Systems & Equipment (heat pumps)
- AHRI 210/240 (EER and COP rating of heat pumps)
Frequently Asked Questions
Why must temperatures be in kelvin for the Carnot COP?
The Carnot COP is a ratio of absolute temperatures, Th/(Th−Tc), so both must be expressed in kelvin (°C + 273.15). Using Celsius directly gives wrong, often negative, results because the formula divides by the temperature lift.
What is a realistic Carnot efficiency for a heat pump?
Real vapour-compression heat pumps achieve roughly 40–55% of the Carnot limit because of compressor, motor, and heat-exchanger losses. A value of 0.45–0.50 is a reasonable default; enter a measured rated COP instead if you have manufacturer data.
Why is the heating COP always one more than the cooling COP?
In heating the condenser delivers both the heat absorbed from the source and the compressor work, so Q_hot = Q_cold + W. Dividing by W gives COP_heating = COP_cooling + 1, an exact identity for the same reservoirs.
How does cold weather affect performance?
As the source gets colder the temperature lift grows, so the COP drops; the chart shows this trend. Below a balance point the heat pump may need supplementary resistance heat, which sharply increases running cost.