Heat Pump COP Efficiency Calculator
The Coefficient of Performance (COP) is the key efficiency metric for heat pumps. It represents the ratio of heat energy delivered to electrical energy consumed. A heat pump with COP 3.0 provides 3 units of heat for every unit of electricity, making it 3x more efficient than direct electric resistance heating (COP = 1.0). COP depends on the temperature difference between the heat source (outdoor air or ground) and the heat sink (indoor air). This calculator computes both the theoretical Carnot COP and estimates an annual heating cost comparison between your heat pump and a baseline electric resistance heater.
Heat pump COP formulas
Carnot COP = T(hot) / (T(hot) - T(cold)) [temperatures in Kelvin: K = (F - 32) x 5/9 + 273.15]
Real COP = Carnot COP x (Real COP % / 100)
HP Electricity (kWh) = Annual Heat Needed (kWh) / Real COP
Resistance Electricity (kWh) = Annual Heat Needed (kWh) / 1.0
Annual Savings = (Resistance kWh - HP kWh) x Electricity Rate
The Carnot COP formula is derived from the second law of thermodynamics. Real heat pumps achieve 40-60% of Carnot efficiency due to compressor isentropic inefficiency, refrigerant pressure drop, and heat exchanger approach temperature losses (ASHRAE Fundamentals Handbook, Chapter 2).
Understanding HSPF ratings
- HSPF (Heating Season Performance Factor) is the US rating for heat pump heating efficiency over a full season.
- The minimum HSPF for new heat pumps sold in the US is 8.2 (DOE 10 CFR Part 430, effective 2023).
- High-efficiency cold-climate heat pumps achieve HSPF of 10 to 13.
- Convert HSPF to average seasonal COP by dividing by 3.412 (BTU per watt-hour).
- HSPF 8.2 corresponds to a seasonal COP of approximately 2.40, meaning 140% more efficient than resistance heat on average.
Heat pump COP calculator: frequently asked questions
What is the Coefficient of Performance (COP) of a heat pump?
COP is the ratio of useful heat delivered to electrical energy consumed. A heat pump with COP 3.0 delivers 3 kWh of heat for every 1 kWh of electricity used. COP varies with outdoor temperature: it decreases as outdoor temperature drops.
What is HSPF and how does it relate to COP?
HSPF (Heating Season Performance Factor) is a seasonal average efficiency rating used in the US, defined as BTU of heat delivered per watt-hour of electricity consumed over a full heating season. HSPF divided by 3.412 gives the average seasonal COP. Minimum federal HSPF is 8.2 for new heat pumps (DOE 10 CFR Part 430).
How does the Carnot COP relate to real heat pump COP?
The Carnot (theoretical maximum) COP = T_hot / (T_hot - T_cold), where temperatures are in Kelvin. Real heat pumps achieve roughly 40-60% of Carnot COP due to compressor losses, refrigerant properties, and heat exchanger limitations.
At what outdoor temperature does a heat pump become less efficient than electric resistance?
Most air-source heat pumps have a COP that drops below 1.0 at outdoor temperatures around 0 to -10 F (-18 to -23 C), at which point electric resistance heating (COP = 1.0) becomes more efficient. Cold-climate heat pumps (ASHP) maintain COP above 1.0 down to -13 F (-25 C).
What is a good COP for a heat pump?
A COP of 2.0 to 3.5 at 47 F outdoor temperature is typical for standard air-source heat pumps. High-efficiency cold-climate models achieve COP of 3.0 to 4.5 at 47 F. Ground-source (geothermal) heat pumps typically achieve COP of 3.0 to 5.0 year-round due to stable ground temperatures.
Official sources
- U.S. Department of Energy: Heat Pump Systems (DOE Energy Saver).
- DOE 10 CFR Part 430: Energy Conservation Program: Energy Conservation Standards for Consumer Products.
- ASHRAE Fundamentals Handbook: ASHRAE Handbook Online.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.