## Coefficient of Performance and Its Importance to Heat Pumps

Written By

Josh Mitchell

Expert Reviewed By

Holly Curell

Last Updated On

Key Takeaways

• Coefficient of performance is an indicator of how energy efficient your heat pump is. You should always aim to get a unit with as high COP as you can.
• The higher the COP rating, the more efficient the system is and the more performance you get  per watt.
• The higher the COP rating of a heat pump, the lower will be the overall electricity consumption, which in turn would result in lower electrical bills.

Understanding the coefficient of performance (COP) is the key to lowering your energy bills and improving household efficiency.

It shows how well your system works by letting you see what you get out compared to what you put in.

It may sound like a daunting technical term, but trust me, the COP is your secret weapon for maximizing performance and choosing the best systems.

I'm here to make it as simple as possible, and in this guide I'll explain:

• What the COP is and why it matters
• The formula in terms anyone can understand
• And how to determine the relative efficiency so you know your heat pump is performing

## Understanding COP or Coefficient of Performance

The coefficient of performance (commonly called COP) is a measure of how efficiently a device transfers heat.

It’s a ratio of how much cooling or heating output you get for the energy you put in.

The coefficient of performance is commonly used for heat pumps that move heat in and out of your home but can also used on a refrigerator or air conditioner system.

#### What exactly does the coefficient of performance show?

Heating and cooling devices draw energy to function, usually expressed in watts. This electrical energy is then converted into heating and cooling power.

Useful Note:

In mathematical terms, the coefficient of performance (COP) is the output energy divided by input energy.

It shows just how much heating or cooling a device can provide for every unit of energy put in.

For example, if the COP rating was 3, every 1 watt of energy put in provides 3 watts of heating or cooling power.

#### Why does the coefficient of performance matter?

The COP matters because it shows us how effective a cooling or heating system is.

The higher the rating, the more efficient the system performance and the more thermal energy you’ll get for each watt of electricity.

#### A higher coefficient of performance (COP) will mean more heat removed/heat provided and lower operating costs.

COP ratings are mostly used by manufacturers, engineers, and designers to check system performance.

HVAC technicians (like me) also use the COP to gauge the overall efficiency of a heat pump or air conditioner.

By understanding the coefficient of performance, you can make a more informed choice about your heating and cooling system, allowing you to control and reduce your household energy consumption.

#### What's a typical coefficient of performance figure?

The coefficient of performance for residential heat pump systems is usually between 2 and 4, but some geothermal heat pumps can be higher.

Useful Note:

I recommend looking for a minimum COP of 1.5.

#### Finding the coefficient of performance

You should be able to find it in the heating and cooling systems’ specifications or user manuals or by checking the energy label.[1]

I also recommend checking the manufacturer's website if you struggle to find it.

I’ll also show you how to work out the cooling and heating coefficient using the wattage and output.

TL;DR: The COP is a measure of how efficient and well performing your heat pump is. The typical range for newer units is between 2 - 4. Do not use a heat pump with COP lower than 1.5.

## How is COP Related to Heat Pumps?

A heat pump operates differently from an air conditioning system, moving hot and cold air in and out of your home.

There are two modes (heating and cooling), and a heat pump has a coefficient of performance (COP) rating for each.

#### 1. Heating mode

The outdoor coil extracts heat from the outside air (or ‘cold reservoir’), and it’s carried inside by the refrigerant.

The heat is released into the air, and the heat output starts to warm the space.

Sometimes, the system pumps additional heat to raise the relative temperature more quickly.

TL;DR: The heating coefficient of performance represents the heat output generated for each watt of electricity.

#### 2. Cooling mode

The process happens in reverse. Heat from the air indoors is absorbed by the heat pump and released outside (or into the cold reservoir/heat sink).

With the heat removed, the temperature drops.

TL;DR: The cooling coefficient of performance represents the cooling performance for each watt of electricity.

#### Why COP is Used Instead of Efficiency?

The coefficient of performance (COP) is the standard measure of heat pump energy efficiency.

An Energy Efficiency Ratio (EER) is commonly used for air conditioner systems (or other cooling devices) but not typically for heating systems.[2]

A COP rating is more versatile and can be applied for both heating and cooling modes - making it perfect for heat pump systems.

#### Minimum COP Efficiency Standards for Geothermal and Air Source Heat Pumps

There are some government regulations on the minimum efficiency of heat pump systems to limit power consumption and minimize environmental impact.[3]

You can find the COP rating in your product description/specifications, and I recommend looking for a rating above 1.5.

The below table gives the minimum standards of different types of heat pumps:

Type of Heat Pump

Mode

Minimum Coefficient of Performance (COP)

Air Source Heat Pump

Heating

1.8

Air Source Heat Pump

Cooling

3.4

Geothermal heat pump - closed loop water-to-air

Heating

3.6

Geothermal heat pump - open loop water-to-air

Heating

4.1

Geothermal heat pump - closed loop water-to-water

Heating

3.1

Geothermal heat pump - Direct geo-exchange (DGX)

Heating

3.6

Exhaust Air Heat Pumps

Heating

1.78

Exhaust Air Heat Pumps

Cooling

2.32

Gas Engine Heat Pumps

1.2

Gas Engine Heat Pumps

Simultaneous heating & cooling

1.1

Absorption Heat Pumps

Air-cooling single stage

0.6

Absorption Heat Pumps

Water-cooling two stage

1.0

## How Do You Calculate COP?

### COP Formula

To calculate the coefficient of performance, you need:

• The heating or cooling output (in watts). You can convert this from BTUs here.[4]
• The power input/ electrical power (in watts)

The basic coefficient of performance formula is:

Coefficient of performance = desired output (heating or cooling) in watts / electrical power input (in watts)

The above formula is commonly shown as:

COP = Q / W

Q = heat supplied or removed by the system

W = the work put into the system each cycle (wattage)

The output shows you the ratio for how much heating or cooling is provided for every 1 watt of energy used by the appliance.

Practical example:

Here’s how you work out the coefficient of performance for an air conditioning system that uses 1500 watts and produces 5000 watts:

COP = 5000 / 1500

The COP is 3.33. Each 1 watt of power gives you 3.33 watts of cooling.

### COP Calculation for Heat Pumps

The same coefficient of performance equation is used for heat pumps. However, a reversible heat pump for heating AND cooling, so you need to decide whether your desired output is either:

#### 1.Producing heat (heating mode)

For this mode, use the following equation:

COPℎ = Qh / W

COPℎ = heating COP

Qh = the amount of heat provided (watts).

W = the electrical power used in heating mode (watts).

#### 2.Removing heat (cooling mode)

For this mode, you need the following equation:

COPc = Qc / W

COPc = the amount of cooling provided by the heat pump. It’s best to use watts.

W = the electrical power consumed by the heat pump in cooling/air conditioning mode.

You will end up with two COPs for your heat pump, one for cooling and one for heating.

The COP is typically slightly higher in cooling mode because the principles of thermodynamics mean it takes less work to transport heat to a cold area.

##### Practical example:

Here's how to work out the heating and cooling coefficient of performance for a heat pump that:

Uses 1500 watts

Produces 2500 watts of heating output

Produces 2100 watts of cooling output

#### Heating mode:

COPℎ = 2100 / 1500

The heating coefficient of performance is 1.4.

This means for every 1 watt of electrical power consumed, it provides 1.4 watts of heating.

#### Cooling mode:

COPℎ = 2500 / 1500

The cooling coefficient of performance is 1.67.

This means for every 1 watt of electrical power consumed, it provides 1.67 watts of cooling.

#### COP Calculation for Refrigerators

Calculating the coefficient of performance for refrigerators is the same as for air conditioners.

Refrigerator COP = Cooling output (in watts) / Power input (wattage)

##### Practical example:

If you have a refrigerator that:

Uses 200 watts

Produces 600 watts

Refrigerator COP = 600 / 200

The refrigerator's COP is 3, meaning that every 1 watt of electricity provides 3 watts of cooling.

## Carnot and Lorentz Efficiency Measurement Explained

The Carnot and Lorentz efficiency measurements are ways to work out the theoretical limits of a heat pump system and how close your real-world heat pump gets to the theoretical limit.

You can use the equations to determine how optimized the heat pump system design is.

These equations are typically only used by equipment manufacturers and researchers.

There are two parts to it:

### 1. The Carnot efficiency

The Carnot efficiency (or Carnot cycle machine efficiency) is the theoretical maximum efficiency of your heat pump operating system based on the second law of thermodynamics.

Essentially, it shows you the maximum coefficient of performance your system could achieve.

#### Equation:

Carnot coefficient = Absolute hot reservoir temperature / absolute hot reservoir temperature - absolute cold reservoir temperature.

### 2. The Lorentz efficiency

The Lorentz efficiency shows the ratio between the actual performance of the heat pump and the theoretical maximum (Carnot coefficient).

#### Equation:

Lorentz efficiency = actual co-efficient of performance / Carnot co-efficient of performance

##### Practical example:

Let's say you have a heat pump with an outdoor air temperature of 30°F, an indoor temperature of 70°F, and an actual coefficient of performance of 3.

• The absolute hot reservoir temperature is 70 + 460 = 530 (this absolute temperature is determined by the Rankine scale.[5]
• The absolute cold water reservoir temperature is 30 + 460 = 490

Carnot coefficient of performance = 530 / (530/490)

The Carnot maximum coefficient of performance is 13.25.

Lorentz efficiency = 3 / 13.25

Lorentz efficiency = 0.22

The figure calculated above means the heat pump currently operates at around 22% of the theoretical maximum.

## Factors That Affect COP for Heat Pumps

#### Type of Heat Pump

Heat pumps use different heating/cooling methods, impacting the coefficient of performance (COP).

Air-source and geothermal heat pumps tend to have the highest COP.

In contrast, absorption and ductless mini-split system COPs can vary depending on the heat source.

I recommend checking the performance COP of the type of heat pump before you buy because a higher COP can lead to significant energy savings.

#### How Well Your Space Is Insulated

Well-insulated homes reduce the workload on heat pumps and improve efficiency.

Installing home insulation, like fiberglass or foam boarding, can reduce heat dissipation and temperature difference, improving the COP rating.[6]

#### System Design

Higher COPs equate to higher efficiency, and well-designed, high-quality heat pumps will have a higher COP because they use more efficient components that reduce the amount of heat lost in the process.

Useful Note:

Heat pump technology is evolving quickly, and you’ll typically find that modern heat pumps have a higher COP.

#### Heat Pump Condition

A heat pump’s COP will reduce over time as components wear out and become less efficient.

I recommend performing monthly cleaning and having a professional HVAC technician inspect it annually to keep the COP of the heat pump at optimal levels.

#### Operating Conditions/Temperature Difference

A larger temperature difference between the indoor (input temperature) and outside (output temperature) temperatures will reduce the coefficient of performance (COP).

Similarly, high humidity and low airflow can reduce the COP as the heat pump has to work harder.

In more extreme conditions, you should expect to have a lower COP rating.

TL;DR: The COP can be impacted by several factors some of which are external to the heat pumps such as environmental factors. Observing best practices such as maintaining regularly can help improve the COP of your unit.

##### What is the Difference Between EER and COP?

The Energy Efficiency ratio (EER) and coefficient of performance (COP) both measure efficiency.

However, EER is used for air conditioners/cooling systems only, and COP is used for heating and cooling systems because it's more versatile.

##### How Does Heat Pump COP Vary with Temperature?

The heat pump’s COP rating is closely linked to temperature.

The greater the temperature difference, the lower the COP efficiency because the heat exchange becomes less efficient.

In heating mode, a lower outside temperature will typically decrease the COP. In cooling mode, a higher outside temperature will lower the COP.

##### Can the COP be Negative?

No, the COP will always be 0 or above because it’s a ratio of two positive quantities - heating/cooling output to electrical power input.

References:

1. https://www.energystar.gov/
2. https://www.energy.gov/energysaver/room-air-conditioners
3. https://www.energystar.gov/products/heat_pumps_geothermal/key_product_criteria
4. https://www.rapidtables.com/convert/power/BTU_to_Watt.html
5. https://www.britannica.com/science/Rankine-temperature-scale
6. https://www.energy.gov/energysaver/insulation
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Josh Mitchell

Founder

My name is Josh and I am obsessed with home appliances. From portable AC units to heaters and air purifiers, I enjoy testing, learning and using these devices to improve the air quality inside my family home.

My Favorite Home Appliance?

Midea U Shaped Window Air Conditioner

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