Coefficient of Performance (COP) Calculator
Find the coefficient of performance of a refrigerator or heat pump, compute the Carnot (ideal) COP from reservoir temperatures, and see how efficiently your device uses electrical work to move heat.
W
W
K
K
Heat removed from cold space per unit of work input (Q_C / W)
- 1
Heat delivered to hot side (Q_H)
3,000 + 1,000 = 4,000Energy conservation: Q_H = Q_C + W. - 2
COP — Refrigerator
3,000 ÷ 1,000 = 3
How does this calculator work?
COP_refrigerator = Q_C / W (cold-side heat removed ÷ work input); COP_heat_pump = (Q_C + W) / W. The ideal Carnot COP_ref = T_C / (T_H − T_C) in Kelvin sets the theoretical ceiling. Enter the heat flows and temperatures to get both COPs and see how the actual COP compares to the Carnot limit.
Formula
How this is calculated
The coefficient of performance (COP) measures how much useful thermal energy is moved per unit of electrical work consumed. For a refrigerator or air conditioner, COP_ref = Q_C / W — heat removed from the cold side divided by work input. For a heat pump delivering warmth indoors, COP_hp = Q_H / W where Q_H = Q_C + W (energy conservation). A typical domestic refrigerator achieves COP 2–4; a modern heat pump 3–6.
The Carnot COP is the theoretical maximum any device can achieve between two reservoirs at absolute temperatures T_C (cold) and T_H (hot), both in Kelvin: Carnot COP_ref = T_C / (T_H − T_C). No real device can equal or exceed this — friction, heat leaks and non-ideal compression all reduce COP below the Carnot limit. The closer the two temperatures, the higher the Carnot limit, which is why heat pumps become less efficient during extreme cold snaps.
Temperatures must be in Kelvin (K = °C + 273.15). Dividing the actual COP by the Carnot COP gives the second-law efficiency — a 100% second-law efficient machine would be a Carnot engine, which is physically impossible. Real high-efficiency systems reach 60–80% of the Carnot limit.
Frequently asked questions
COP is not an efficiency capped at 100%. A refrigerator moves heat that already exists in the cold space — it does not create energy from nothing. Because it moves more thermal energy than the electrical work it consumes, COP > 1 is normal and expected for well-designed systems.
Both use the same thermodynamic cycle, but the useful output differs. A refrigerator's useful effect is the heat Q_C removed from the cold side; a heat pump's is the heat Q_H delivered to the warm side. Since Q_H = Q_C + W, we always have COP_hp = COP_ref + 1 — a heat pump COP is one unit higher than the same device running as a refrigerator.
No. The Carnot COP is an absolute upper bound set by the second law of thermodynamics. A result above Carnot means a measurement error, an incorrect energy balance, or temperatures stated in the wrong units. Real devices always fall below the Carnot limit.
Also known as
TG we-Calculate Editorial Team. (2026). Coefficient of Performance (COP) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/performance-coefficient-calculator
TG we-Calculate Editorial Team. "Coefficient of Performance (COP) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/performance-coefficient-calculator.
TG we-Calculate Editorial Team, "Coefficient of Performance (COP) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/performance-coefficient-calculator
@misc{wecalculate_performance_coefficient_calculator, title = {Coefficient of Performance (COP) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/performance-coefficient-calculator}}, year = {2026}, note = {TG we-Calculate} }
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