Refrigeration capacity and efficiency

tons of refrigerationCOPEERkW per tonchiller efficiencygpm per ton

Tons, COP, EER and kW per ton — the four ways the trade states the same chiller performance, and how to convert between them.

Tons of Refrigeration from BTU/hr

T = \frac{\dot{Q}}{12{,}000\ \text{BTU/hr}}

Converts a cooling load in BTU/hr (or kW) to tons of refrigeration, where one ton is 12,000 BTU/hr or 3.5169 kW.

Coefficient of Performance (COP)

\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}

Efficiency of a heat pump or chiller: useful heating or cooling delivered divided by the electrical power drawn to deliver it.

Energy Efficiency Ratio (EER)

\mathrm{EER} = \frac{\dot{Q}\ [\text{BTU/hr}]}{\dot{W}\ [\text{W}]}

Cooling efficiency as BTU/hr of capacity per watt of electrical input, a deliberately mixed-unit ratio equal to 3.412 times the COP.

EER to COP Conversion

\mathrm{EER} = 3.412 \times \mathrm{COP}

Converts between the two efficiency scales, since one watt of input equals 3.412 BTU/hr and both ratios describe the same machine.

Chiller Efficiency (kW per Ton)

\mathrm{kW/ton} = \frac{\dot{W}\ [\text{kW}]}{\dot{Q}\ [\text{tons}]}

The chiller-plant efficiency metric: kilowatts drawn per ton of cooling produced, where lower is better and 0.5 kW/ton is excellent.

Condenser Water Flow Rate

\dot{V} = \frac{\dot{Q} \cdot \mathrm{HRF}}{\rho_w c_w \, \Delta T}

Tower water flow needed to reject a chiller's load plus compressor heat, the physics behind the 3 gpm per ton at 10 °F rule of thumb.

How they fit together

A ton of refrigeration is a historical unit — the rate that melts one short ton of ice in 24 hours, 12,000 BTU/hr — and everything else here is capacity divided by input power in different clothes. COP is dimensionless (watts out per watt in). EER is BTU/hr out per watt in, so EER = 3.412 × COP. kW per ton is the same ratio inverted, which is why lower is better: 0.6 kW/ton is an excellent water-cooled chiller, 1.2 kW/ton is a tired one.

Choose by who is reading the number. Engineers and anyone working in SI use COP; equipment nameplates and rating standards use EER or SEER; chiller plant operators live in kW/ton because it multiplies straight into a utility bill. Two traps. First, published efficiencies are at rated conditions — a chiller quoted at 0.55 kW/ton at AHRI conditions will not hold that with 95 °F condenser water on a design day, and part-load IPLV numbers are a weighted average you will never actually operate at. Second, kW/ton on a plant meter must state its boundary: compressor-only, or compressor plus tower fans plus condenser and chilled water pumps. The second number is often 40% higher, and comparing one against the other is the most common way a retrofit is made to look like it worked.