Cop Formula

Coefficient of Performance (COP) Formula

Every appliance that people buy has some level of efficiency, and people choose to buy them depending on that level. The coefficient of performance is a key component in assessing how efficient air conditioners, refrigerators, and heat pumps are. When we go to the store to purchase an air conditioner, refrigerator, or heat pump, the first thing we look for is the COP value. Let’s look deeper at the Coefficient of Performance (COP) formula.

How to calculate COP Formula

Heat dissipation and electrical power intake determine the Coefficient of Performance (COP). An air conditioning unit’s performance is evaluated by this parameter. The Coefficient of Performance (COP) is the ratio of heat dissipation to electrical power intake. It is the parameter used to assess the performance of an air conditioning machine. It demonstrates how effective heating and cooling systems are. The following points highlight the features of COP.

  1. This is the ratio of compressor power input to refrigeration output.
  2. As the coefficient of performance (COP) rises, the cooling output increases in proportion to the power input.
  3. Efficiency increases with an increase in COP.
  4. Efficiency increases as COP rises, and efficiency decreases as COP falls.
  5. It is the ratio between the evaporator’s cooling output and the air conditioner’s or refrigerator’s work input.
  6. The higher the COP, the higher the power consumption, and the higher the running costs.

Formula of Coefficient of Performance (COP)

The Coefficient of Performance is calculated as follows,

COP = Output / Input


Coefficient of Performance for heating is,

K = QH / Win


K = Coefficient of Performance,

QH = The heat pump’s output,

Win = The work required by the considered system.


Coefficient of Performance for cooling is,

K = QC / Win


K = Coefficient of Performance,

QC = the refrigerator’s heat had dissipated,

If the Work input is zero then the Coefficient of Performance is equal to infinity.


COP of Refrigerator is,

KR = Q2 / (Q1 – Q2)

For reversible Refrigerator,

Q1/Q2 = T1/T2

KR = T2 / (T1 – T2)


COP of Heat pump,

KH = Q1 / (Q1 – Q2)

For reversible Heat pump,

Q1/Q2 = T1/T2

KH = T1 / (T1 – T2)

Sample Questions

Example 1: An air conditioning system operates between a high temperature of 300 K and a low temperature of 250 K. Find the Coefficient of Performance (COP) for the air conditioner.

Solution: Given: T 1 ​ =300K (high temperature), T 2 ​ =250K (low temperature)

Using the Coefficient of Performance Formula K R ​ = T 2/ (T 1 ​ −T 2 ​ ) ​ ​ ,

K R ​ = 250 ​/ (300−250)

K R ​ = 250 ​ / 50

K R ​ =5

Therefore, the Coefficient of Performance (COP) for the air conditioner is 5.

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FAQs (Frequently Asked Questions)

1. What is the COP S.I. unit?

It has no units.

2. Is a higher or lower COP preferable?

The higher the coefficient of performance, the more efficient the system.

3. What happens to COP if the work input is zero?

If the work input is zero, the COP becomes infinite.