Engineering
Heat Pump & Chiller COP (Cooling vs Heating) & EER HVAC formulas
Calculate cooling Coefficient of Performance COP_cool = Q_cold / W_in, heating COP_heat = (Q_cold + W_in) / W_in = COP_cool + 1, and Energy Efficiency Ratio EER = 3.41214 * COP.
Use the same operating point and system boundary
Cooling COP is removed thermal power divided by input power, using the same units. This is heat moved per unit of input, not conversion efficiency. A heat pump can move more heat than its work input without creating energy.
The identity COPheat=COPcool+1 holds for the same steady cycle boundary when all input work and extracted heat are rejected to the hot side, with no unaccounted losses. It does not let you infer a product’s rated heating COP from its rated cooling COP at different conditions. Include the appropriate fans, pumps and controls when calculating a whole-system rating.
EER in Btu/(W h) is approximately3.41214 times cooling COP at the same boundary and conditions; the factor is rounded, not exact. SEER/SEER2 are seasonal measures with defined test procedures and cannot be obtained from one operating-point COP. This worksheet does not calculate a certified EER2 or SEER2 rating.
Changing input from3 to2.1 kW while holding cooling output fixed is a hypothetical scenario, not a prediction of inverter part-load performance. Both inputs must be numeric, cooling output nonnegative and work input strictly positive.
| HVAC Performance Metric | Formula | Illustrative cooling10.5 kW, input3.0 kW | Hypothetical same output, input2.1 kW |
|---|---|---|---|
| Cooling COP_cool | B2 / B3 | 10.5 / 3.0 = 3.50 | 10.5 / 2.1 = 5.00 |
| Heating COP_heat (First Law) | (B2 + B3) / B3 | 13.5 / 3.0 = 4.50 (COP_cool + 1!) | 12.6 / 2.1 = 6.00 |
| Energy Efficiency Ratio (EER) | 3.41214 * (B2 / B3) | 11.94 BTU/(Wh) | 17.06 BTU/(Wh) |
Cooling COP
Both inputs must share identical power units (e.g., both in kW or both in Watts).
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<0,B3<=0),"Invalid inputs",ROUND(B2 / B3, 2)))Convert Cooling COP to North American EER (BTU / Wh)
Convert cooling COP at the same operating point using the approximate Btu-per-watt-hour factor. This is not a seasonal efficiency calculation.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<0,B3<=0),"Invalid inputs",ROUND(3.41214 * (B2 / B3), 2)))Heating COP for the same ideal energy balance
Use only the same system boundary and operating point described above.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<0,B3<=0),"Invalid inputs",ROUND((B2 + B3) / B3, 2)))Try the example
Use the original values or change them to test your understanding.