liminfoHeat Pump COP Calculator
Free web tool: Heat Pump COP Calculator
Carnot COP (Ideal)
15.13
Real COP (~45% Carnot)
6.81
Electrical Input
1.55 kW
Cost (HP vs Resistance)
$0.186/hr vs $1.266/hr
Energy Savings vs Resistance
85.3%
COP at Different Outdoor Temps
-10°F
2.98
0°F
3.41
10°F
3.97
20°F
4.77
30°F
5.96
40°F
7.95
50°F
11.92
About Heat Pump COP Calculator
The Heat Pump COP Calculator computes the Coefficient of Performance (COP) of a heat pump based on outdoor and indoor temperatures, using Carnot thermodynamic theory. You enter the outdoor temperature (°F), indoor temperature (°F), heating capacity (BTU/h), and electricity rate ($/kWh). The calculator first derives the ideal Carnot COP as Th / (Th - Tc), where Th and Tc are the indoor and outdoor absolute temperatures in Kelvin. It then estimates the real-world COP as 45% of the Carnot COP — a standard engineering approximation that accounts for compressor inefficiency, heat exchanger losses, and refrigerant cycle irreversibilities. This 0.45 multiplier is representative of modern variable-speed heat pumps operating in typical conditions.
The tool is used by homeowners evaluating heat pump systems, HVAC engineers comparing heating technologies, energy auditors, and building performance analysts. The key output is the percentage energy savings compared to electric resistance heating (which has a COP of exactly 1.0 by definition). A heat pump with a real COP of 2.5 uses only 40% of the electricity that a resistance heater would need to produce the same heat output — a 60% savings. The calculator also shows the hourly operating cost for both the heat pump and a resistance heater at the same capacity, making the economic comparison concrete.
An additional table shows the estimated real COP across seven outdoor temperatures from -10°F to 50°F, keeping the indoor set temperature fixed. This illustrates the fundamental characteristic of heat pumps: COP decreases as outdoor temperature drops because the temperature differential widens, requiring the compressor to work harder. At very low outdoor temperatures, COP can approach 1.0, at which point an auxiliary resistance strip heater becomes the more practical option. All calculations run entirely in your browser with no server calls.
Key Features
- Carnot COP calculation from outdoor and indoor temperatures converted to Kelvin
- Real-world COP estimated at 45% of Carnot COP for a practical efficiency approximation
- BTU/h to kW conversion for heating capacity (1 BTU/h = 0.000293071 kW)
- Hourly operating cost comparison: heat pump vs electric resistance heater
- Percentage energy savings of heat pump over resistance heating displayed prominently
- COP table across 7 outdoor temperatures (-10°F to 50°F) at fixed indoor temperature
- Electrical input power (kW) required by the heat pump displayed as a key output
- Fully client-side — no energy or cost data is transmitted to any server
Frequently Asked Questions
What is COP for a heat pump?
COP (Coefficient of Performance) is the ratio of heat energy delivered to electrical energy consumed. A heat pump with COP 3.0 delivers 3 kWh of heat for every 1 kWh of electricity used. Unlike electric resistance heating (COP = 1.0), a heat pump moves heat from outside rather than generating it, which is why COP can exceed 1.
What is the Carnot COP and how is it calculated?
The Carnot COP is the theoretical maximum efficiency for a heat pump operating between two temperatures. It is calculated as Th / (Th - Tc), where Th is the hot reservoir (indoor) temperature and Tc is the cold reservoir (outdoor) temperature, both in Kelvin (°C + 273.15). No real heat pump can exceed the Carnot COP.
Why is the real COP estimated at 45% of Carnot?
Real heat pumps cannot achieve the Carnot ideal due to compressor inefficiency, refrigerant pressure losses, heat exchanger temperature approach, and motor losses. Studies and manufacturer data suggest that well-designed heat pumps typically achieve 40–50% of Carnot COP. This calculator uses 45% as a representative middle estimate. Actual COP varies by equipment type and operating conditions.
How does outdoor temperature affect heat pump COP?
COP decreases as outdoor temperature drops because the temperature difference (Th - Tc) widens, requiring more compressor work per unit of heat delivered. At 50°F outdoor temperature, a heat pump might have a COP of 3–4, but at -10°F it might be 1.5–2. Below about 5–15°F, many air-source heat pumps use supplemental resistance heating.
How much energy does a heat pump save vs electric resistance heating?
Savings equal (1 - 1/COP) × 100%. A heat pump with COP 2.5 saves (1 - 1/2.5) × 100% = 60% compared to resistance heating. At COP 3.0 it saves 67%, at COP 4.0 it saves 75%. The calculator displays this savings percentage prominently along with hourly cost for both options.
What does heating capacity in BTU/h mean?
BTU/h (British Thermal Units per hour) is the rate at which a heating system delivers heat. A common residential heat pump might be 24,000–60,000 BTU/h (2–5 tons). The calculator converts BTU/h to kW (1 BTU/h = 0.000293071 kW) to compute electrical input power at the given COP.
Why are the temperatures entered in Fahrenheit if the calculation uses Kelvin?
The input fields use Fahrenheit because it is the standard unit for HVAC in the US market. The calculator internally converts to Kelvin by applying (°F - 32) × 5/9 + 273.15 before applying the Carnot formula. The result is the same regardless of which temperature scale is used for input, as long as the conversion is correct.
What types of heat pumps does this calculator apply to?
This calculator applies primarily to air-source heat pumps, which are the most common type for residential heating. Ground-source (geothermal) heat pumps generally achieve higher COP because ground temperature is more stable than air temperature in winter. The 45% of Carnot COP approximation is most representative of modern inverter-driven air-source units.