Can COP be greater than 1?

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.

Why does COP decrease in cold weather?

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.

Is a heat pump always better than a furnace?

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.

What is a ground-source heat pump?

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.

COP / Performance Coefficient Calculator

Calculate coefficient of performance for heat pumps, refrigerators, and air conditioners. Compare actual COP to Carnot limit with SEER/EER conversion.

Mode

Hot Side Temperature (°C)

Cold Side Temperature (°C)

Electrical Power Input (kW)

Thermal Output (kW) — optional

COP (Actual)

5.50

Heat delivered / work in

Carnot COP (Heating)

11.01

Th / (Th − Tc)

Carnot COP (Cooling)

10.01

Tc / (Th − Tc)

Carnot Efficiency

50.0%

COP_actual / COP_Carnot

Heat Delivered

5.50 kW

COP × Win

SEER / EER

18.8 BTU/Wh

COP × 3.412

Savings vs Resistance

82%

Electricity saved over COP=1

ΔT

28.0 K

Th − Tc

COP vs Carnot Limit

50% of Carnot

Typical COP Values

Device	COP Range	Notes
Room air conditioner	2.5−3.5	Window/split unit cooling
Central AC (SEER 16)	3.5−4.7	Seasonal average COP
Air-source heat pump	2.5−4.5	Depends on outdoor temp
Ground-source heat pump	3.5−5.5	Stable ground temperature
Refrigerator	1.5−3.0	Domestic fridge/freezer
Industrial chiller	3.0−6.0	Centrifugal or screw type
Carnot (ideal)	∞ at ΔT→0	Theoretical upper limit

Planning notes, formulas, and examples

About the COP / Performance Coefficient Calculator

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.

When This Page Helps

COP analysis is the foundation of HVAC system comparison and energy cost estimation. It provides Carnot limits and real-world COP analysis.

It helps homeowners choose between heat pump and resistance/furnace heating, and engineers optimize refrigeration system design.

How to Use the Inputs

Select heating (heat pump) or cooling (refrigerator/AC) mode.
Enter the hot and cold side temperatures in °C.
Enter the electrical power input in kW.
Optionally enter the actual thermal output — otherwise the calculator estimates it.
Read the actual COP, Carnot COP, and efficiency percentage.
Compare with the typical COP table for your device type.

Formula used

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%.

Example Calculation

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.

Tips & Best Practices

Ground-source heat pumps have stable COP year-round because ground temperature barely changes.
Defrost cycles in air-source heat pumps reduce effective COP by 5-15% in cold weather.
Variable-speed compressors maintain higher COP at part load than on/off units.
For fair comparison, convert SEER → COP: divide by 3.412.
A COP of 3 means 67% of the heat is "free" — extracted from the environment.

When To Use This Calculator

Calculate coefficient of performance for heat pumps, refrigerators, and air conditioners. Compare actual COP to Carnot limit with SEER/EER conversion. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

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.