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Refrigerator COP Calculator

Find a refrigerator's coefficient of performance.

Result

11.00

How it is calculated

This is the ideal (Carnot) coefficient of performance of a refrigerator, the upper limit any real machine can reach: COP = T_cold / (T_hot - T_cold). T_cold is the temperature of the cold space and T_hot the temperature of the surroundings it rejects heat to, both in kelvin (K = °C + 273.15). The temperatures must be absolute, T_cold above 0 and T_hot greater than T_cold, otherwise the tool returns nothing. COP is dimensionless: heat removed from the cold space per unit of work put in. A real refrigerator reaches only a fraction of this value because of friction, pressure drops and non-ideal compressors.

Worked example

A fridge interior at 275 K (about 1.85 °C) in a kitchen at 300 K (about 26.85 °C). The temperature difference is 300 - 275 = 25 K. COP = 275 / 25 = 11.00. In the ideal case, each unit of work moves 11 units of heat out of the fridge. A real unit might reach 2 to 4, so the Carnot figure is a ceiling, not a prediction.

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Common mistakes

  • Entering Celsius values like 4 and 25. They must be converted to kelvin first, otherwise COP comes out wrong.
  • Swapping hot and cold. The hot temperature must be the larger one, or the tool returns no result.
  • Expecting the Carnot COP to match the label of a real appliance; real devices are well below it.
  • Confusing refrigerator COP with heat-pump COP. For heating the formula uses T_hot in the numerator.

About this calculator

This calculator finds the theoretical maximum coefficient of performance of a refrigerator, the Carnot COP = T_c/(T_h−T_c), where T_c and T_h are the cold and hot reservoir temperatures in kelvin. COP measures how much heat is removed from the cold space per unit of work input — a value that can exceed 1, unlike a simple efficiency ratio — and the Carnot limit represents the absolute best any refrigeration cycle could achieve between those two temperatures, a direct consequence of the second law of thermodynamics.

HVAC and refrigeration engineers use this Carnot benchmark to see how far a real refrigerator's or air conditioner's actual COP falls short (a heat pump in heating mode is compared with the related limit T_h/(T_h−T_c)) of the theoretical ceiling, which highlights where a design has room for efficiency improvement. Appliance designers use it during early-stage design to set realistic performance targets, and thermodynamics students use this calculator to connect the abstract Carnot cycle to a device they use every day.

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Comments (1)

  • Editorial team

    Compare a fridge and a freezer in a 25 °C room. The fridge at 4 °C gives a Carnot COP of about 13.20, while a freezer at -18 °C gives about 5.93, so the colder box has a much lower ceiling. Real condenser coils run warmer than the room air, so using room temperature is the most optimistic case. Convert Celsius to kelvin first. Do you have measured temperatures from a real appliance to compare against?

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