Heat Pump COP Calculator
Find the maximum theoretical coefficient of performance (COP) of a heat pump from its hot and cold reservoir temperatures, COP=Th/(Th-Tc).
🏠 What is the Heat Pump COP Calculator?
This heat pump COP calculator finds the maximum theoretical coefficient of performance from COP=Th/(Th−Tc). Enter the hot (heated space) and cold (heat source) temperatures in Kelvin, and it returns the Carnot (reversible) maximum COP and the equivalent refrigeration-mode COP.
With Th=300 K and Tc=250 K, this calculator gives exactly COP=6, meaning a perfect heat pump could deliver 6 units of heat for every 1 unit of work input.
Heat pump COP is always exactly 1 higher than the equivalent refrigeration COP for the same two temperatures, since both use the identical underlying cycle.
This calculator is useful for thermodynamics and HVAC engineering students evaluating the theoretical performance ceiling of heat pump heating systems.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Classic textbook benchmark
Example 2 - Mild-climate heating (small gap)
Example 3 - Cold-climate heating (larger gap)
❓ Frequently Asked Questions
🔗 Related Calculators
What is heat pump COP?
Heat pump coefficient of performance (COP) measures how much heat is delivered to a space per unit of work (typically electricity) input, unlike simple resistance heating (COP=1 at best), a heat pump moves existing heat rather than creating it, allowing COP values well above 1.
What is the formula for the maximum theoretical heat pump COP?
COP_HP = Th/(Th−Tc), where Th and Tc are the absolute (Kelvin) temperatures of the hot (heated space) and cold (heat source) reservoirs. This is the Carnot (reversible) COP, the theoretical maximum for any heat pump operating between those two temperatures.
How is heat pump COP related to refrigeration COP?
They use the exact same cycle: COP_HP = COP_R + 1, always exactly 1 higher than the refrigeration COP for the same two temperatures, since the heat delivered to the hot side always exceeds the heat removed from the cold side by exactly the work input.
Why can heat pump COP exceed 1, unlike combustion or resistance heating?
A heat pump doesn't create heat from the work input, it uses that work to move existing heat from a colder source (like outdoor air or ground) into the heated space, so the heat delivered can be several times larger than the work input, unlike resistance heating which converts at most 100% of input energy to heat.
Why does heat pump performance drop in cold weather?
As the outdoor (cold-side) temperature Tc drops further below the indoor target Th, the temperature gap (Th−Tc) grows, directly lowering COP per the formula, this is why air-source heat pumps become less efficient (and some switch to backup heating) in very cold climates.
What is a typical real-world COP for a heat pump?
Real air-source heat pumps typically achieve COPs of 2-4 under moderate conditions, well below their theoretical Carnot maximum, ground-source (geothermal) heat pumps often achieve higher real-world COPs since ground temperature stays more stable than outdoor air temperature.
Can any real heat pump reach the Carnot COP?
No, like the Carnot heat engine and refrigerator, the Carnot heat pump cycle assumes perfectly reversible operation with no friction or irreversible heat transfer, conditions no real system achieves. Real heat pumps achieve a fraction of this theoretical maximum.
Why are heat pumps often described as more efficient than furnaces?
A gas furnace can approach but never exceed 100% combustion efficiency (COP effectively capped near 1), while a heat pump moving heat rather than generating it can achieve COPs of 2-4 or more, delivering multiple units of heat per unit of electrical energy consumed.
Does the heated-space temperature affect heat pump COP?
Yes, per the formula, a higher target indoor temperature Th (for the same outdoor Tc) increases the temperature gap, lowering COP, this is one reason lowering your thermostat setting slightly can meaningfully improve heat pump efficiency.
What units does this calculator use?
Both reservoir temperatures must be entered in Kelvin (absolute temperature). COP itself is dimensionless.