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How to Calculate Coefficient of Performance

By Nordic

August 05, 2015

Heat Pump Installation

heat pump cop
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You’ve probably heard that geothermal heat pumps are the most efficient way to heat and cool your home. But what does that phrase actually mean for your home and your heating bills? What does energy efficiency mean? How is it measured? How is it calculated? What is heat pump COP? That’s what we’re going to look at today.

Efficiency is how much energy you get out of an appliance, compared to how much energy you put into running it. A 97% efficient furnace gives you back 97% of the energy you put into it in the form of heat for your home, the other 3% is lost up the flue. Since electric baseboard has no flue, 100% of the energy that goes in, stays in your home in the form of heat. The higher the efficiency of your system, the lower your heating bills.

Keep reading to learn about geothermal heat pump efficiency, how to calculate it, and what it means for your home heating bills.

Calculating Your Geothermal Heat Pump COP

Geothermal heat pump efficiency is traditionally measured using a ratio called “coefficient of performance” (COP). The COP of a geothermal heat pump is the ratio of the heating or cooling output to the energy input to run the machine. A high COP over 1.0 means your heat pump is performing very efficiently, and your heating bills will be low. A heat pump is the only heating and cooling device that has a COP over 1.0.

Let’s take a deeper look at how to calculate a heat pump’s heating COP.

Calculating Coefficient of Performance

First, you’ll need two things:

  1. Energy out, or the heat pump’s expected output.
  2. Energy In, or how much energy it takes to run the heat pump.

Using these two values, we can complete the formula below:

COP

In this formula, energy out is the heat pump’s output in Btu/hr, and energy in is the energy required to run the heat pump, measured in watts.

Let’s do an example calculation using our standard four-ton water to air heat pump. All of the information we need is available in this heat pump’s manual, found on the R Series product page. The data we need is on page 35 of the manual.

A four-ton water to air heat pump operating in heating mode on a closed ground loop has an output of 35,900 Btu/hr when the compressor is running in stage 2. The first thing we need to do is convert the Btu/hr output to watts. One Btu/hr equals 0.293 watts.

35,900 Btu/hr x 0.293 = 10,518 watts

Now we have the “energy out” portion of the formula in watts, and from the manual, we see that the heat pump consumes 2,700 watts to run. This is the “energy in” part of the COP formula.

Now we can plug this into the calculation: COP = energy out / energy in

COP = 10,518 / 2,700 = 3.89

Based on our calculations, a four-ton water to air heat pump running in heating mode on stage 2 would have a COP of 3.89. That means for every watt of electricity used to run this machine; you’ll get 3.89 watts of heat energy out of the heat pump. The extra output is free energy harvested from the ground loop by the heat pump. Put in terms of the efficiency we mentioned above, a four-ton R Series heat pump is 389% efficient when heating in stage 2.

Coefficient of Performance and Your Home’s Heating Bills

Compared to electric baseboard or an oil furnace, geothermal is very, very efficient. The high COP means you’ll have lower heating bills, but just how much lower?

We’ve put together a table comparing the efficiencies of electric baseboard heating, geothermal heating and an air to water heat pump, and the effect on your heating bills:

Electric BaseboardAir Source Heat PumpGeothermal Heat Pump
COP1.002.923.89
Efficiency100%292%389%
Yearly Electric Consumption$4,000$1,369$1,028

Coefficient of Performance And Changing Conditions

Your heat pump’s COP changes depending on operating conditions, here are several factors that will affect your heat pump’s effective COP: 

Whether It’s Heating or Cooling Season

Since the output of the heat pump changes when in cooling mode, so does the COP. If you look in our manuals, we calculate separate COPs for every heat pump in both heating (COPh) and cooling (COPc) modes to account for this variance.

Whether the Heat Pump is in First or Second Stage

All Nordic heat pumps have two-stage scroll compressors, which allows the heat pump to vary its output depending on the heating or cooling demands. Since the output changes depending on which stage the heat pump is operating in, the formula changes, and so does the resulting COP. Our manuals account for this and we calculate separate COP’s for each stage.

For example, the four-ton water to air heat pump we looked at above has a COP of 4.10 in stage 1 and 3.89 in stage 2 while in heating mode on a closed loop. You can estimate an average COP by adding these two together and dividing by two:

(4.20 + 3.89) / 2 = 4.05

 Individual Operating Conditions

There are myriad individual operating conditions that affect the actual COP of your heat pump. Variables like the temperature of your ground loop, the temperature of the buffer tank (if you’re using in-floor heat) and whether or not you’re on an open or closed loop all affect the actual COP of your heat pump.

Fortunately all of these variables will have a minimal effect on the actual performance of your heat pump, and you can rely on the reported COP’s in our heat pump manuals as a baseline for how your system will perform when it is installed correctly, or as in the example above, you can calculate it yourself!

Looking for more information on how geothermal heating can reduce your home’s utility bills by up to 75%? Download our Free Ebook: Geothermal Energy: Consistent, Comfortable and Cost Effective.

Download Now




Photo Credit

Comments

  1. Reply

    Patrick Servidio

    February 14, 2018

    Dear Sir, I have a general question, after leaving
    the pool heat pump at what temperature is the actual pool water temperature retuning back to the Swimming pool? Example, pool water temperature is 75 F going into heat pump at what temperature will it heat the pool water? 5F 10F or
    more degrees Fahrenheit?

    • Jordann Brown

      February 15, 2018

      Hi Patrick, do you have a Nordic heat pump? If so please include the model number and serial number and I’ll let you know the answer to your question.

  2. Reply

    Leo

    November 07, 2018

    Your chart doesn’t make sense. Natural Gas is currently around $0.38/100,000 BTU. Electric is around $3.50/100,000 BTU. Even if you have a 5 COP, heat pump will be twice as expensive as a 97% efficiency natural gas furnace.

    • Jordann Brown

      November 08, 2018

      Hi Leo, here is the source link for that chart: http://mse.coopwebbuilder2.com/sites/msemse/files/images/heat-pump-chart.jpg
      We did not generate it but I assume that they took local utility costs into consideration. Remember that the price of natural gas and electricity will vary dramatically from region to region, which will affect the overall cost of each type of system.

  3. Reply

    Peter Mac

    November 13, 2018

    Does the COP increase with higher bore hole temp (for heating)
    My ground source (2x 150mtr boreholes) give 9.6C constant.
    My heatpump unit is set to 25C
    Is there a link to a graph to show the efficiency?

    • Jordann Brown

      November 13, 2018

      Hi Peter, changing the source temperature and the output temperature of the heat pump will affect the efficiency. You can see the performance of the heat pump at different source temperatures in the product manual. I don’t know which type of heat pump you have, but just for reference, here is our standard water to air heat pump manual, you can find these types of efficiencies on page 50: https://www.nordicghp.com/wp-content/uploads/2018/10/001200MAN-08-R-Series-Two-Stage-R410a.pdf

  4. Reply

    Arturo Diego

    February 10, 2019

    How much energy is saved in terms of kWh heat and kWh electricity?

    • Jordann Brown

      February 12, 2019

      Hi Arturo,
      That number would depend on your current energy consumption, where you are located, what your original heat source was, and which heat pump you are switching to. As you can see, it’s not a straight forward answer, but if you’d like us to get into that you can email info@nordicghp.com for more details.

  5. Reply

    Zvi Klier

    April 04, 2019

    If I can use a constant flow of water at 35 C on the reference side (like geothermal) and heat water constantly from 50 to 65 deg C what would be the actual COP? thanks

    • Jordann Brown

      April 04, 2019

      Hi Zvi,
      You can find performance ratings are similar input/output temperatures in our WH Series product manuals: https://www.nordicghp.com/product/nordic-products/high-temp-water-to-water/wh-series/

  6. Reply

    Gilbert Fabian Rodriguez Rodriguez

    September 04, 2019

    Dear Jordann

    I have two question, you can help me clarify them please.

    1. How i can calculating the thermal energy used in a heat pumps
    2. How I can calculating the Cooling Energy for a heat pump.

    Thank you a lot for you response

    Best Regards

    Gilbert Rodriguez

    • Jordann Brown

      September 04, 2019

      That information is available on our product manuals, which you can find on each product page.

  7. Reply

    Tim Morse

    October 15, 2019

    How does the power used to pump the water figure in to the COP performance of the system? It seems there is a lot additional power being consumed to provide water to the system

    • Jordann Brown

      October 23, 2019

      Hi Tim,
      Apologies for the delayed response but I believe one of my colleagues answered your question via email.

  8. Reply

    Joseph M Schnerr

    October 29, 2019

    How about large commercial applications? I have a winery and we are looking to expand. I’d have a total of 7500 ft2 of well insulated warehouse room that I want to operate at 55 degrees F year round (for barrels and case goods). Do you have experience with any units that are scaled for that sort of work?

    • Jordann Brown

      October 30, 2019

      Hi Joseph,
      We have a full roster of commercial geothermal heat pumps that would work for your application. I’d recommend submitting a contact form on our website, you’ll be put in touch with one of our engineers who can offer guidance which heat pumps would be a suitable fit.

  9. Reply

    John Wright

    March 31, 2022

    What cop will you get at 15°c ambient, at what cop will you get at -2°C ambient. Is it considerably less so that is why electric back up heaters are required. What happens when in coastal areas the outdoor coil freezes a lot quicker, does that mean more defrost cycles are required, more ice on the outdoor coil means cop deficiency . Possibly more honesty in the capability of heat pumps should be forth coming.

    • Dan Rheault

      April 08, 2022

      Hi, air source heat pumps will have a lower capacity and COP when it is colder outside. This is the reason they require auxiliary heat, whereas a geothermal heat pump has the same capacity and COP all year round so can be sized to 100% of the heat load and won’t require auxiliary heat.

      You are right in that with an air source heat pump, more defrosts will be required in humid areas.

      When it is 15°C outside, you will get a COP of ~4.0 (depending on indoor water temperature), and when it -2°C outside that COP will drop to ~3.0. There are detailed performance tables in the manuals and specifications on our website if you’d like more detailed performance information.

  10. Reply

    Dominic

    February 20, 2023

    All of these calculations for cost depend on the current price of nat gas vs electricity. Where are these numbers in the examples given?

    • Dan Rheault

      February 20, 2023

      Hi, it’s easy to compare the energy usage of a geothermal heat pump with electric heat, since electric heat has a COP of 1.0. So if you are running a heat pump with a COP of say 4.0, you will use 1/4 the energy. Natural gas is a little more complex to compare, since its cost relative to electricity fluctuates and its COP is less than one (perhaps ~85% or 0.85). It is possible to use a spreadsheet to do a comparison, maybe a topic for a future article.

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