What is the Coefficient of Performance of a refrigerator?

COP is the ratio of heat removed from the cold space (Q_cold) to the net work input (W): COP = Q_cold / W. A higher COP means a more efficient refrigerator — it removes more heat per joule of electrical energy consumed.

Can COP be greater than 1?

Yes. Unlike thermal efficiency (which is always ≤ 1), COP can be well above 1 because the refrigerator moves heat rather than converting it. A typical household refrigerator has a COP of 2–6.

What units should I use?

Q_cold and W must use the same units — both in joules (J), watts (W), BTU, or kilowatts. The COP is dimensionless.

How does refrigerator COP relate to heat pump COP?

For the same cycle, COP_heat_pump = COP_refrigerator + 1. The heat pump COP counts the heat delivered to the hot reservoir (Q_hot = Q_cold + W), while refrigerator COP counts only Q_cold.

What is the maximum possible COP?

The Carnot COP sets the upper bound: COP_Carnot = T_cold / (T_hot − T_cold), where temperatures are in Kelvin. Real refrigerators always have a lower COP due to irreversibilities.

Refrigerator COP Calculator

Enter heat absorbed from the cold reservoir and work input to calculate refrigerator COP.

Inputs

Unit system

Heat absorbed from cold reservoir — Q_cold (J)

Net work input — W (J)

Compare with Carnot COP (optional)

Enter reservoir temperatures to see the theoretical maximum COP.

Cold reservoir temperature T_cold (K)

Hot reservoir temperature T_hot (K)

Results

Enter values and click Calculate

Formula reference

Refrigerator COP

COP = Q_cold / W

Energy balance

Q_hot = Q_cold + W

Carnot COP (max)

COP_c = T_cold / (T_hot − T_cold)

Summary

The Coefficient of Performance (COP) of a refrigerator measures how efficiently it moves heat from a cold reservoir to a hot reservoir per unit of work consumed. A COP greater than 1 means the refrigerator moves more heat than it consumes in work — typical household refrigerators have a COP between 2 and 6. This tool computes COP = Q_cold / W, where Q_cold is the heat absorbed from the cold reservoir and W is the net work input.

How it works

Enter the heat absorbed from the cold reservoir (Q_cold) in joules or kilowatts.
Enter the net work input (W) consumed by the refrigerator in the same units.
The calculator applies COP = Q_cold / W to compute the result.
Results include COP, heat rejected to the hot reservoir (Q_hot = Q_cold + W), and an efficiency rating.
Adjust any value and results update instantly.

Use cases

Check the COP of a household refrigerator or freezer.
Compare the efficiency of different refrigeration systems in engineering coursework.
Verify thermodynamics homework problems involving refrigeration cycles.
Evaluate COP against the ideal Carnot COP for a given temperature range.
Estimate heat rejected by a refrigerator into the surrounding room.
Design HVAC systems by assessing compressor work vs. cooling load.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu