3.3333
6,500
J
5,000
J
3.3333
×
3.3333
6,500
J
5,000
J
3.3333
×
The Coefficient of Performance (COP) Calculator evaluates the efficiency of refrigerators, air conditioners, and heat pumps. Unlike heat engines that produce work, these devices consume work to transfer heat from one reservoir to another. The COP measures how effectively they accomplish this heat transfer relative to the work consumed.
For a refrigerator or air conditioner, the COP is defined as the ratio of heat removed from the cold space to the work input: $$\text{COP}_{\text{cool}} = \frac{Q_c}{W}$$ For a heat pump, the COP is the ratio of heat delivered to the warm space to the work input: $$\text{COP}_{\text{heat}} = \frac{Q_h}{W}$$
A key distinction from heat engine efficiency is that COP values are typically greater than 1. A heat pump with a COP of 4.0 delivers 4 joules of heat for every 1 joule of electrical energy consumed. This means heat pumps can be 3–5 times more energy-efficient than direct electric resistance heaters, which have a COP of exactly 1.0.
The relationship between heating and cooling COP follows from energy conservation: since $$Q_h = Q_c + W$$, we get $$\text{COP}_{\text{heat}} = \text{COP}_{\text{cool}} + 1$$. This means the heating COP is always greater than the cooling COP by exactly one unit for the same device.
This calculator is essential for HVAC engineers sizing heating and cooling equipment, energy auditors comparing system performance, appliance buyers evaluating Energy Star ratings, and thermodynamics students learning the principles of refrigeration cycles. Enter the heat transferred and work input to get instant COP calculations along with the complementary heat transfer and energy multiplier values.
Modern residential heat pumps achieve COP values of 3–5 under typical conditions, while industrial chillers can reach COP values of 5–7. Ground-source (geothermal) heat pumps tend to have higher COP than air-source units because ground temperatures are more stable throughout the year.
The COP calculator uses fundamental energy balance equations for refrigeration and heat pump cycles:
Refrigerator / Air Conditioner COP:
$$\text{COP}_{\text{cool}} = \frac{Q_c}{W}$$
where $$Q_c$$ is the heat removed from the cold reservoir and $$W$$ is the work input (compressor power).
Heat Pump COP:
$$\text{COP}_{\text{heat}} = \frac{Q_h}{W}$$
where $$Q_h$$ is the heat delivered to the warm space.
Energy Conservation:
$$Q_h = Q_c + W$$
For cooling mode, the calculator computes $$Q_h = Q + W$$ (heat rejected to outdoors). For heating mode, it computes $$Q_c = Q - W$$ (heat absorbed from outdoors).
Equivalent Efficiency: The inverse of COP, $$1/\text{COP}$$, represents what fraction of the heat transfer would be needed as work input, useful for comparison with engine efficiency.
The COP value indicates how many units of heating or cooling you get per unit of work (electricity) consumed. A COP of 3.5 for a refrigerator means 3.5 joules of heat are removed from the interior for every joule of electricity the compressor uses. For a heat pump with COP 4.0, you get 4 joules of heat delivered for every joule of electricity. Higher COP means lower operating costs. The 'Other Heat Transfer' shows the complementary energy flow: for cooling mode, it shows heat rejected outdoors; for heating mode, it shows heat absorbed from outdoors. The energy multiplier confirms how many times more useful energy you get compared to direct electric heating or cooling.
Inputs
Results
An air conditioner removes 5000 J of heat from a room using 1500 J of electrical work. The COP is 3.33, meaning 3.33 units of cooling per unit of electricity. The total heat rejected outdoors is 6500 J (5000 absorbed + 1500 from compressor work).
Inputs
Results
A geothermal heat pump delivers 8000 J of heat to the house using 2000 J of electricity. The COP is 4.0, meaning it is 4 times more efficient than a resistance heater. It absorbs 6000 J from the ground to achieve this.
For air conditioners and refrigerators, a COP of 3–5 is typical. For heat pumps, COP of 3–5 is common for air-source units and 4–6 for ground-source (geothermal) units. Higher COP means lower energy costs. Energy Star rated appliances generally have above-average COP for their category. Note that COP varies with operating conditions—it decreases as the temperature difference between reservoirs increases.
COP measures the ratio of useful heat transfer to work input, not the ratio of energy output to total energy input. A heat pump doesn't create energy—it moves heat from one place to another using work. Since the heat delivered includes both the heat absorbed from outside plus the compressor work, the output (Q_h) always exceeds the input (W). This is perfectly consistent with energy conservation: Q_h = Q_c + W.
EER (Energy Efficiency Ratio) and SEER (Seasonal EER) are used in the HVAC industry and are related to COP but use different units. EER = cooling capacity (BTU/h) ÷ power input (W). To convert: COP = EER ÷ 3.412. SEER is a seasonal average that accounts for varying outdoor temperatures. A SEER of 14 corresponds to a seasonal average COP of about 4.1.
Yes, significantly. COP decreases as the temperature difference between the hot and cold reservoirs increases. An air-source heat pump has a higher COP on a mild day (5°C outdoor) than on a frigid day (−15°C). This is why ground-source heat pumps maintain better COP—underground temperatures remain relatively constant year-round (10–15°C in most climates).
The maximum COP is given by the Carnot COP: COP_cool,max = T_c/(T_h − T_c) and COP_heat,max = T_h/(T_h − T_c), where temperatures are in Kelvin. For a refrigerator at 5°C (278 K) with outdoor temperature 35°C (308 K), the Carnot COP is 278/30 = 9.27. Real devices achieve 30–50% of the Carnot COP.
Not exactly. Efficiency (η) is defined as useful output divided by total input and is always ≤ 1 (100%). COP is defined as desired heat transfer divided by work input and can exceed 1. For a heat engine, η = W/Q_h ≤ 1. For a heat pump, COP = Q_h/W ≥ 1. They are related: COP_heat = 1/η_Carnot for reversible cycles. The term 'coefficient of performance' is used instead of 'efficiency' precisely because COP > 1 would be misleading if called efficiency.
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The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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