Refrigerator COP Calculator
The coefficient of performance (COP) of a refrigerator measures how efficiently it moves heat from a cold space to a warmer environment. The Carnot COP represents the theoretical maximum achievable with a perfect thermodynamic cycle operating between two temperature reservoirs. The formula COP = Tc / (Th - Tc), where temperatures are in Kelvin, gives this upper limit. Real refrigerators always have a lower COP due to irreversibilities. This calculator is used in thermodynamics coursework, HVAC engineering, and energy efficiency analysis of refrigeration equipment.
Carnot COP formula
COP(refrigerator) = Tc / (Th - Tc) COP(heat pump) = Th / (Th - Tc)
Tc and Th must be in Kelvin (K = degrees C + 273.15). COP(HP) = COP(ref) + 1 always holds for the same cycle. The Carnot efficiency of the equivalent heat engine is: eta = 1 - Tc/Th.
Worked example
- Freezer at -10 degrees C (263 K), kitchen at 25 degrees C (298 K).
- COP = 263 / (298 - 263) = 263 / 35 = 7.51 (theoretical Carnot maximum).
- A real household freezer typically achieves COP of 1.5 to 2.5.
Frequently asked questions
What is the coefficient of performance (COP) of a refrigerator?
COP is the ratio of the heat removed from the cold reservoir (Qc) to the work input (W): COP = Qc / W. A higher COP means more cooling per unit of electrical energy consumed. The Carnot COP sets the theoretical maximum.
What is the Carnot COP formula for a refrigerator?
The Carnot (maximum) COP for a refrigerator is COP_Carnot = Tc / (Th - Tc), where Tc is the absolute temperature of the cold reservoir and Th is the absolute temperature of the hot reservoir. Temperatures must be in Kelvin.
What COP do real refrigerators achieve?
Typical household refrigerators achieve COP of 1.5 to 2.5. Commercial refrigeration systems may reach 3 to 5. The Carnot COP (calculated here) is an upper theoretical limit that no real device can exceed.
How does this differ from COP of a heat pump?
For a heat pump, COP_HP = Th / (Th - Tc). This is always exactly 1 higher than the refrigerator COP, because a heat pump is the same cycle run for heating rather than cooling.
Why must temperatures be in Kelvin?
Kelvin is the absolute thermodynamic temperature scale. Using Celsius or Fahrenheit would give physically incorrect results because the formula involves the ratio of temperatures, which is only meaningful on an absolute scale.
Official sources
- ASHRAE: ASHRAE Handbook of Fundamentals (Thermodynamics).
- OpenStax University Physics: 4.4 Second Law and Carnot Engine.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.