Heat Pump Coefficient of Performance: The COP Formula and Reference Table
The heat pump coefficient of performance, or COP, is the single most important measure of industrial heat pump performance. It is a dimensionless ratio of energy output to energy input, both expressed in heat equivalents. For an electrically driven machine the formula is:
COP = Thermal Output (Btu/hr) divided by (Power Input (kW) x 3,413 Btu/kWh)
A 50 kW heat pump delivering 1,000,000 Btu/hr therefore has a COP of 5.86. A higher COP means more heat moved per unit of work, which converts directly into lower operating cost and lower emissions.
Heat Pump Coefficient of Performance Reference Table
| COP | Electricity Required (kWh per million Btu) | Heat Drawn from Source | Cost per Million Btu at $0.06/kWh |
| 2.00 | 146.5 | 50% | $8.79 |
| 2.50 | 117.2 | 60% | $7.03 |
| 3.00 | 97.7 | 67% | $5.86 |
| 3.50 | 83.7 | 71% | $5.02 |
| 4.00 | 73.2 | 75% | $4.39 |
| 4.50 | 65.1 | 78% | $3.91 |
| 5.00 | 58.6 | 80% | $3.52 |
| 5.50 | 53.3 | 82% | $3.20 |
| 5.86 | 50.0 | 83% | $3.00 |
| 6.00 | 48.8 | 83% | $2.93 |
| 6.50 | 45.1 | 85% | $2.70 |
| 6.92 | 42.3 | 86% | $2.54 |
| 7.00 | 41.9 | 86% | $2.51 |
| 7.50 | 39.1 | 87% | $2.34 |
| 8.00 | 36.6 | 88% | $2.20 |
Electricity required is 1,000,000 divided by (3,413 x COP). The third column is (COP minus 1) divided by COP, the share of delivered heat recovered from the source rather than supplied by the compressor. The $0.06/kWh rate is illustrative only and must be replaced with the site tariff.
Estimating COP Before You Have a Machine
At feasibility stage, COP can be approximated from refrigerant temperatures:
COP = 0.6 x (460 + Tcond) divided by (Tcond minus Tevap), temperatures in degrees Fahrenheit
The 0.6 factor reflects typical industrial equipment efficiency and rises with machine size. Critically, Tcond and Tevap are refrigerant temperatures, not water temperatures. A machine producing 120F hot water while cooling a tower stream to 85F will condense around 128F and evaporate around 77F, allowing roughly 8F of approach at each exchanger. That gives 0.6 x 588 divided by 51, or a COP of 6.92. Using the water temperatures directly returns 9.94, which no industrial machine will achieve. This distinction is where most feasibility estimates go wrong.
Reading COP as an Energy Balance
The same ratio sets the energy balance. Heat recovered from the source equals heat delivered times (COP minus 1) divided by COP. At a COP of 6.92, 86 percent of the delivered heat is recovered waste heat and only 14 percent comes from the compressor. Invert the expression to size deliverable heat from an available recovery stream, which is the usual starting point on an EPC retrofit.
Frequently Asked Questions
What is a good COP for an industrial heat pump?
Typical open cycle industrial machines fall between 4 and 7 depending on temperature lift. The smaller the gap between condensing and evaporating temperature, the higher the achievable COP.
How much electricity does a heat pump need?
Divide the heating duty by 3,413 times the COP. At a COP of 6.92, one million Btu/hr requires 42.34 kW.
Does a higher COP always mean lower cost?
Not necessarily. If the machine runs through peak demand periods, the demand charge can outweigh the energy saving. Interrupting operation during peak windows often improves the economics more than chasing COP.
Heat recovery only pays when the numbers are built on site measured temperatures and the actual tariff. USP&E Global has delivered 150+ projects across 35+ countries, and our power plant engineering and hybrid power systems teams model COP as part of every efficiency study, with monitoring through SmartPower. Industrial electricity rate and efficiency data is published by the U.S. Energy Information Administration, the International Energy Agency, and the U.S. Environmental Protection Agency.
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