Heat Pump and Chiller COP Calculator: Capacity and Running Cost against Outdoor Temperature
An estimate of how the COP and capacity of an air-source heat pump or chiller change with the outdoor temperature, and what it costs to run.
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How this calculator works
A heat pump moves heat from a cold source to a warm destination, and the bigger the temperature difference it works across, the harder it works. The most efficient a machine can ever be between two temperatures is the Carnot COP. A real machine reaches a share of it, about 0.4 to 0.55 for a good air-source machine.
The calculator takes the outdoor air temperature and the delivery temperature, allows a temperature approach at each heat exchanger (the evaporator must be colder than the outdoor air and the condenser hotter than the delivery temperature), finds the Carnot COP between them, and multiplies by the share you enter.
The capacity of a heat pump also falls as the outdoor air gets colder, just when the building needs most heat. The calculator estimates this from the rated capacity at 7 degrees and a percentage change per degree, so you can see whether the machine covers the load on the coldest day and what it costs to run. These figures are estimates: the maker's data for the real machine always wins.
Formulas used
- COP_{Carnot,heat} = \frac{T_c}{T_c - T_e}
- COP_{Carnot,cool} = \frac{T_e}{T_c - T_e}
- COP = \varepsilon_C\,COP_{Carnot}
- P = Q_d / COP
Worked example
With the default numbers in the calculator above:
- Evaporating and condensing temperatures (with the approach): -6 and 48 °C
- Carnot COP between them: 5.947
- Estimated COP of the machine: 2.676
- Electrical power to meet the load: 7.473 kW
- Capacity at this outdoor temperature: 21.88 kW
- Running cost at this load: 17.94 $/day
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Why is a low delivery temperature better?
The temperature lift is smaller, so the COP is higher. A floor heating or fan coil system at 35 degrees gives a much better COP than radiators at 60 degrees.
What COP should I expect?
It depends on the machine and the temperatures. Use the maker's data at your outdoor and delivery temperatures; this tool shows the trend.
Does it include defrost?
No. Defrost cycles in cold, damp weather lower the real average COP and capacity.
Related calculators
Further reading: ASHRAE Handbook: HVAC Systems and Equipment; Cengel and Boles, Thermodynamics: An Engineering Approach; Moran and Shapiro, Fundamentals of Engineering Thermodynamics.
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