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03 // Bidirectional STEM Calculators // ENGINEERINGCOP = Q_thermal / W_in

Coefficient of Performance (COP) Heat Pump & Chiller Solver

The Coefficient of Performance (COP) measures heat pump or chiller efficiency as the ratio of useful thermal heat moved Q_thermal to electrical compressor work input W_in: COP = Q_thermal / W_in.

COP = Q_thermal / W_in
Pick which value you want to calculate (or type into any field):Solving for: COP — Coefficient of Performance
Calculated

Thermal Watts moved per electrical Watt consumed

0.512
unit

Thermal capacity in Watts (switch unit to kW)

1001,000,000.00

Electrical power consumed in Watts (switch unit to kW)

50500,000.00
Calculated Result · Coefficient of Performance (COP)
3.8

Step-by-Step Calculation

01Canonical Law: COP = Q_thermal / W_in
02Given Inputs (Base Units): Q_thermal = 11,400 W, W_in = 3,000 W
03Solve for COP (Coefficient of Performance): COP = 3.8

The Coefficient of Performance (COP) measures heat pump or chiller efficiency as the ratio of useful thermal heat moved Q_thermal to electrical compressor work input W_in: COP = Q_thermal / W_in.

Real-World Reference Values

Electric Resistance BaseboardCOP = 1.00

1 kW electricity produces exactly 1 kW heat

Inverter Air-Source Heat PumpCOP = 3.2 – 4.5 (at 7 °C)

Moves 3.2–4.5× more heat energy than electricity used

Centrifugal Water-Cooled ChillerCOP = 5.5 – 7.0

EER = COP × 3.41214 BTU/(Wh)

20-Row Comparison Table

Coefficient of Performance (COP) · Thermal Heating/Cooling Output (Q_thermal)

Coefficient of Performance (COP) Heat Pump & Chiller Solver — Thermal Heating/Cooling Output → Coefficient of Performance
#Thermal Heating/Cooling Output (W)Coefficient of Performance (COP)Δ %
01100 W0.033333 -99.12%
0211,400.00 WCurrent3.8 0.00%
0315,761.71 W5.2539 +38.26%
0423,592.57 W7.8642 +106.95%
0531,423.42 W10.4745 +175.64%
0639,254.28 W13.0848 +244.34%
0747,085.13 W15.695 +313.03%
0854,915.99 W18.3053 +381.72%
0962,746.84 W20.9156 +450.41%
1070,577.70 W23.5259 +519.10%
1178,408.55 W26.1362 +587.79%
1286,239.41 W28.7465 +656.49%
1394,070.26 W31.3568 +725.18%
14101,901.12 W33.967 +793.87%
15109,731.97 W36.5773 +862.56%
16117,562.83 W39.1876 +931.25%
17125,393.68 W41.7979 +999.94%
18133,224.54 W44.4082 +1068.64%
19141,055.39 W47.0185 +1137.33%
20148,886.25 W49.6288 +1206.02%
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Frequently Asked Questions

How can a heat pump have a COP greater than 1.0 (over 100%) without violating conservation of energy?+

A heat pump does not create heat from electricity alone; it uses 1 unit of electrical work to pump 2.5 to 3.5 units of existing ambient heat from outside to inside.

How do I convert COP to EER (Energy Efficiency Ratio)?+

Multiply COP by 3.41214 (since 1 Watt = 3.41214 BTU/hr). A COP of 3.8 equals an EER of 12.97.

How do I convert COP to kW/ton for commercial chillers?+

Chiller efficiency in kW/ton equals 12 / EER = 3.51685 / COP.