Heat Pump COP and Energy Balance Calculator
Calculate heating and cooling coefficients of performance and compare heating COP with a reversible reservoir-temperature limit.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Divide delivered heat by electrical input, recover cold-side heat from energy balance and compare the result with the reversible Carnot heating COP.
Heating COP=Qhot/W; cooling COP=heating COP−1; Carnot heating COP=Thot/(Thot−Tcold)
Worked example
Delivering 4 kW with 1 kW input gives heating COP 4 and extracts 3 kW from the cold side. Reservoirs 0°C and 40°C give an ideal heating COP limit 313.15/40≈7.82875.
Assumptions and input details
Steady heat-pump energy balance with hot-side heat at least electrical input. Reservoir temperatures must be above absolute zero, hot greater than cold, and are converted to kelvin. Device surface or air temperatures may differ from thermodynamic reservoir assumptions. Values above the ideal bound are explicitly flagged for checking. No defrost, seasonal average, auxiliary heating, installation performance or manufacturer rating is inferred.
References: OpenStax: refrigerators and heat pumps
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
SI prefixes are explicit: for example, milli means one thousandth, micro one millionth and kilo one thousand. Changing a unit changes the interpretation of the entered number.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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