Calculate coefficient of performance for heat pumps, refrigerators, and air conditioners. Compare actual COP to Carnot limit with SEER/EER conversion.
The Coefficient of Performance (COP) measures the efficiency of heat pumps, refrigerators, and air conditioners. It is the ratio of useful heating or cooling output to the electrical work input. Unlike thermal efficiency (0-100%), COP can exceed 1 because these devices move heat rather than convert it.
For heating, COP = Qhot/W. For cooling, COP = Qcold/W. The theoretical maximum is the Carnot COP, which depends only on the temperature difference between hot and cold sides. Real devices achieve 30-60% of the Carnot limit.
This calculator computes both actual and Carnot COP for heating and cooling modes, converts to SEER/EER ratings used in US standards, and estimates energy savings compared to electric resistance heating. A reference table shows typical COP values for common devices.
Understanding COP is essential for HVAC system selection, energy auditing, and thermodynamic analysis. A ground-source heat pump with COP = 4.5 delivers 4.5 kW of heat for every 1 kW of electricity — saving 78% compared to resistance heating.
COP analysis is the foundation of HVAC system comparison and energy cost estimation. This calculator provides instant Carnot limits and real-world COP analysis.
It helps homeowners choose between heat pump and resistance/furnace heating, and engineers optimize refrigeration system design. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
COP_heating = Qh / W. COP_cooling = Qc / W. Carnot heating: COP_Carnot,h = Th / (Th − Tc). Carnot cooling: COP_Carnot,c = Tc / (Th − Tc). SEER = COP × 3.412 BTU/Wh. Energy savings: (1 − 1/COP) × 100%.
Result: Carnot COP = 11.0, Estimated actual COP ≈ 5.5, Savings ≈ 82%
Carnot: (35+273.15)/(35−7) = 11.0. At 50% Carnot efficiency: COP ≈ 5.5. This means 5.5 kW of heat per 1 kW electricity. Savings = (1 − 1/5.5) × 100% = 82% vs resistance heating.
Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.
Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes
Use this for repeatability, keep assumptions explicit. ## Practical Notes
Track units and conversion paths before applying the result. ## Practical Notes
Use this note as a quick practical validation checkpoint. ## Practical Notes
Keep this guidance aligned to the calculator’s expected inputs. ## Practical Notes
Use as a sanity check against edge-case outputs. ## Practical Notes
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Yes! COP routinely exceeds 1 because heat pumps and ACs move heat, not convert energy. A COP of 4 means you get 4 kW of heating per 1 kW of electricity — the extra energy comes from the environment.
SEER (Seasonal Energy Efficiency Ratio) measures AC efficiency in BTU per watt-hour over a season. SEER ≈ COP × 3.412. A SEER 16 unit has an average COP of about 4.7.
Larger temperature differences reduce the Carnot limit. At −15°C outdoor and +35°C indoor (ΔT = 50 K), Carnot COP = 6.2. At +7°C outdoor (ΔT = 28 K), it is 11.0. Real devices follow this trend.
EER is measured at a single rated condition (35°C/26.7°C). SEER is a seasonal average over a range of temperatures. SEER is always higher than EER for the same unit.
In mild climates, heat pumps easily beat gas furnaces in cost. In extreme cold (below −10°C), COP drops below 2-3, and a gas furnace may be more economical depending on electricity vs gas prices.
It uses the stable underground temperature (10-15°C year-round) as the heat source/sink. This smaller temperature difference gives much higher COP (3.5-5.5) than air-source units in extreme weather.