Informational Guide

Coefficient of Performance Explained

Learn more about COP in heat pumps in our complete guide. We explain about coefficient of performance and how it relates to HVAC systems.

by Josh M

A heat pump system is more reliable and efficient than a furnace or an air conditioner; it’s also an energy-efficient choice.

However, heat pump systems come in different heating or cooling efficiencies. To get the right unit for your cooling/heating needs, make sure to look at the coefficient of performance(COP) rating!

COP is the most widely used energy efficiency measurement system for heat engines. It is used to compare the performance of air conditioners, refrigerators, and heat pumps.

Read on as we elaborate on COP and how it works.

Co-efficient of performance or COP is a measure to assess how effectively a heat pump employs electricity to transfer heat from one side to another.

Mainly, a heat pump’s COP is a ratio between heating and the power consumed.

To put it simply, the coefficient of performance (COP) measures the amount of heat energy moved in contrast to the amount of heat energy used.

For instance, an air-source heat pump has a COP of 2.5, meaning that it transfers heat energy 2.5 times more than the energy consumed.

Lastly, an adequate co-efficient of performance for a heat pump unit begins at 2 (air-source heat pump) and approximately 3.1 (geothermal heat pump). It can also be above 4!

COP Thermodynamics: How Heat Pumps Work

The working principle of a heat pump is similar to various kinds of cooling units. It is also the complete opposite of how a heat engine works. This assessment may seem a bit complicated; however, it isn’t!

Typically, heat pumps move energy to the heat sink from the heat source; however, in this situation, the transfer happens in reverse. It extracts heat from the outdoors (cold space) and pumps it indoors (warmer space).

It basically works like a refrigerator; the heat pump uses electricity to transfer heat from a cool area and add it to your indoor environment.

This phenomenon is better illustrated below:

The fundamental principle of working – Heat Pump

Here’s the equation to calculate COP:

COP (heating) = Q (hot)/W =Q (cold) +W/ W

For ideal heat pumps that have no irreversibility’s and losses, the equation can be:

COP (heating) = T (hot) / T (hot) – T (cold)

Different Types Of Heat Pumps Explained

Geothermal Heat Pumps

Geothermal or ground-source heat pumps utilize heat energy stored in the ground around your house and transfers it indoors.

These pumps are costlier to install; however, they have considerably low running cost because of consistent ground temperatures.

Some of the advantages of geothermal heat pumps include:

  • Reduced energy consumption by 30-60%
  • Manages humidity
  • Reliable and sturdy
  • It can easily fit into various homes

Nevertheless, geothermal or ground source heat pumps usually have a COP between 3 and 5.

Air To Water Heat Pumps

The most widely used heat pumps are the air to water heat pumps that transfer heat from the outside air and pass it to the water that moves through your indoor underfloor heating systems or radiators. Plus, it can be used to heat water that circulates to your hot water tank.

These heat pumps can reduce power consumption by 50% in comparison to the baseboard and furnace heaters. Also, an air-to-water heat pump is typically less expensive to install than a geothermal heat pump.

The COP of air to water heat pumps can be around 2 to 3.3.

Calculating Co-efficient Of Performance

Heat Pump – COP Calculation

Here’s how you can calculate the Coefficient Of Performance (COP) for a heat pump:

COP heat pump = T (hot) / (Thot – Tcold)

T (hot) denotes the hot temperature you want during cold weather conditions (95F or 298K). On the contrary, T (cold) indicates cold temperature where your heat pump begins to function (57F/ 287K).

So, maximum theoretical efficiency COP can be calculated as:

Heat Pump’s COP = 298K / (298 K – 287 K) is equal to 27.09

Therefore, in theoretical terms, heat pumps can have COPs even greater than 20. However, in actual terms, it is considerably lower.

The standardized test to calculate COP of the heat pump can be:

T-hot is equal to 95 F (308 K) 

T-cold is equal to 32 F (273 K) 

This result indicates that in a perfect scenario, a heat pump’s optimum COP should be 8.8; however, it’s much lower in practical terms. The highest COP that heat pumps can actually attain is approximately 4.5, and heat pumps with a higher COP than 3 are considered high energy-efficient pumps.

Refrigerator – COP Calculation

Here’s how you can calculate the COP of your refrigerator:

By applying the law of thermodynamics, the formula for cooling devices (refrigerators and air conditioners) can be:

COP (cooling) = T (cold) / (Thot – Tcold)  

T (cold) denotes low temperature, whereas T (hot) implies high-heat temperature.

Let’s have a look at the COP of refrigerators in the standard temperature intervals:

T (hot) = 95F (308K)

T (cold) = 32F (273K)  

By applying these in the above cooling COP equation, you get 7.8.

If you’re looking to buy a refrigerator, make sure you purchase a unit with the COP value well above 2.

Methods Of Measuring Coefficient Of Performance

Carnot Efficiency

Carnot efficiency is the maximum theoretical efficiency of the heat pump. It can be calculated by employing the following equation:

COP (h, Carnot) = T cond [K] / T cond – T evap

The formula indicates that Carnot-efficiency is based on the evaporation and condensation temperature. With a perfect compression cycle (without losses), it’s entirely possible to attain Carnot efficiency.

But, in practical terms, the Carnot efficiency can be adversely affected due to numerous variables. So the realistic COP (h) can be described as:

COP (h) = n. COP h, Carnot

Note: System efficiency can be around 50-70%.

Lorentz Efficiency

As it lacks a condensation temperature, Carnot-efficiency can’t be used with a trans-critical CO2 heat pump.

The maximum theoretical efficiency of a trans-critical CO2 heat pump can be described in terms of Lorentz Efficiency as:

COP h, Lorentz = Tm [K] / Tm [K] – T evap [K]

Tm denotes the mean temperature. It’s measured from the temperatures at the outlet and inlet of a gas cooler.

Tm = T gc, in [K] – T gc, out [K] / ln (Tgc,in [K] / Tgc,out [K])

Like the Carnot-efficiency, Lorentz-efficiency is also not achievable because of various losses.

A system efficiency should be considered to determine actual COP:

COP (h) = n.COP h, Lorentz

People Also Ask (FAQ)

How Can I Increase COP For Heat Pumps?

The Coefficient of Performance (COP) of heat pumps can be increased by minimizing temperature difference, improving the house’s insulation, using correct flooring and a ground-source heat pump system when possible.

Can The COP Of Heat Pump Be Greater Than 1?

The COP of heat pumps typically exceeds 1 because it converts work-to-heat and pumps additional heat when needed.

Where Can I Find A COP For A Refrigerator?

We have described it above, but in a nutshell, the formula to find the COP of a refrigerator is COP (cooling) = T (cold) / (Thot – Tcold). What it may be depends on the outside temperature and desired indoor temperature. If the said difference is around 25°C, the COP should be somewhere about 2.5, whereas if the variance is of 8 °C, the COP may be approximately 3.5

What Is The Heat Pump Formula In Terms Of Temperature?

The heat pump system formula in terms of temperature is COP = Q/W. Know that Q denotes useful heat removed or supplied, and W implies the work needed.

What Is The Heat Pump COP Curve?

The Coefficient of Performance (COP) for the heat pump system can also be expressed in the form of a curve, which shows the power consumed to operate the equipment against the amount of heat energy supplied.


Heat pumps are an effective way to meet your heating and cooling needs in colder climates.

And knowing how to calculate COP is the best way to prepare yourself to make a purchase.

The COP is a performance rating, which tells you how effective your heat pump system or a refrigerator is at moving heat against the power consumed.

The higher the COP, the efficient the unit is!

Josh M

My name is Josh and I am obsessed with the HVAC industry. I created this website to help HVAC techs of all levels get the best out of their heating & cooling systems. I have spent thousands of hours studying air conditioners, heaters and home air products so you can learn & buy with confidence. Learn more about the team here.