Quick answer
A heat pump's coefficient of performance is COP = heat delivered ÷ electrical input. Delivering 9 kW of heat with 2.4 kW of electricity gives a COP of 3.75; the Carnot limit is T_h ÷ (T_h − T_c) in kelvin.
Choose a mode and enter the heat output and electrical input (or temperatures). The calculator returns the COP.
Related tools: Specific Heat Calculator: Specific heat capacity or heat required from Q = m c ΔT. Heat Transfer Calculator: Conductive heat flow through a flat wall. Thermodynamic Processes Calculator: Work, heat and internal energy for an ideal gas process.
How to use the Heat Pump COP Calculator
- Choose use: From heat output and power input and Carnot (ideal) heating limit.
- Optionally, enter heat delivered (kW) (above 0).
- Optionally, enter electrical input (kW) (above 0).
- Optionally, enter hot side temperature (°C).
- Optionally, enter cold side temperature (°C).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Use | Choose one: From heat output and power input; Carnot (ideal) heating limit | Starts at From heat output and power input |
| Heat delivered (optional) | A number, in kW | > 0 |
| Electrical input (optional) | A number, in kW | > 0 |
| Hot side temperature (optional) | A number, in °C | — |
| Cold side temperature (optional) | A number, in °C | — |
Formula and method
Formula
COP = Q_out ÷ W_in; Carnot COP = T_h ÷ (T_h − T_c) in kelvin
IEEE-754 double precision; shown to the decimals indicated.
The Carnot value is an upper limit that real machines cannot reach.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Use = From heat output and power input; Heat delivered = 9; Electrical input = 2.4.
| Result | Value |
|---|---|
| COP | 3.75 |
Example 2
Inputs: Use = Carnot (ideal) heating limit; Hot side temperature = 35; Cold side temperature = 5.
| Result | Value |
|---|---|
| Carnot COP | 10.2717 |
Example 3
Inputs: Use = From heat output and power input; Heat delivered = 3.5; Electrical input = 1.
| Result | Value |
|---|---|
| COP | 3.5 |
The first line is the headline result (cOP). IEEE-754 double precision; shown to the decimals indicated.
What COP means
A COP of 3.75 means 3.75 units of heat for each unit of electricity, 375% efficiency compared with resistive heating at 100%. It varies with the temperature difference: COP falls as it gets colder outside.
Carnot limit
The ideal COP between 20 °C (293 K) and 0 °C (273 K) is 293 ÷ 20 = 14.65. Real machines reach perhaps 30 to 50% of that. The hot side must be warmer than the cold side.
How the result changes with heat delivered
Holding every other input at the first worked example, this table changes only heat delivered. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Heat delivered | COP |
|---|---|
| 4.5 | 1.875 |
| 9 | 3.75 |
| 18 | 7.5 |
| 36 | 15 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Heat delivered: left empty shows "Enter the heat delivered." beside that field and no result.
- Hot side temperature: entering "5" shows "The hot side must be warmer than the cold side." beside that field and no result.
Choosing between the Heat Pump COP Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Specific Heat Calculator](/science/specific-heat-calculator/) | solve for, mass and temperature change | Specific heat |
| [Heat Transfer Calculator](/science/heat-transfer-calculator/) | thermal conductivity, area and temperature difference | Heat flow |
| [Thermodynamic Processes Calculator](/science/thermodynamic-processes/) | process, gas and amount of gas | Work done by the gas |
| [EER Calculator](/science/energy-efficiency-ratio-calculator/) | cooling capacity and power input | EER |
| [Thermal Expansion Calculator](/science/thermal-expansion-calculator/) | coefficient of linear expansion, original length and temperature change | Change in length |
Background: heat and temperature
The basic heat relation is Q = m × c × ΔT: heat in joules equals mass times specific heat capacity times temperature change. A positive Q means heat absorbed and a negative Q heat released, and a change in °C is numerically the same as a change in K.
It covers a change in temperature only. During melting or boiling the temperature stays constant while heat still flows (latent heat), which needs a separate term.
Assumptions and limitations
- Hot side must be warmer than cold side
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for heat delivered and hot side temperature to confirm this.
Frequently asked questions
What is a good COP?
3 to 4 for air-source heat pumps.
How does outdoor temperature change COP?
It falls as it gets colder.
What is SCOP?
A seasonal average COP.
What does the Heat Pump COP Calculator calculate?
Coefficient of performance from heat output and power input, or the Carnot limit. It returns COP.
What formula does the Heat Pump COP Calculator use?
COP = Q_out ÷ W_in; Carnot COP = T_h ÷ (T_h − T_c) in kelvin. The Carnot value is an upper limit that real machines cannot reach.
What do I need to enter in the heat Pump COP Calculator?
You enter Use. Optional: Heat delivered (kW), Electrical input (kW), Hot side temperature (°C) and Cold side temperature (°C).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Hot side must be warmer than cold side.
What does the “Use” option change?
It sets how the heat Pump COP is worked out. The choices are From heat output and power input and Carnot (ideal) heating limit.
What is an example of a heat Pump COP result?
With use From heat output and power input, heat delivered 9 and electrical input 2.4, the cOP is 3.75.
Related calculators
- Specific Heat Calculator — Specific heat capacity or heat required from Q = m c ΔT.
- Heat Transfer Calculator — Conductive heat flow through a flat wall.
- Thermodynamic Processes Calculator — Work, heat and internal energy for an ideal gas process.
- EER Calculator — Energy efficiency ratio of an air conditioner and its COP equivalent.
- Thermal Expansion Calculator — Change in length from a temperature change.
- Heat Index Calculator — Apparent temperature from air temperature and relative humidity (°F).
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.