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# Refrigeration Formulas

## Calculate compression work, coefficients of performance and more.

### Compression Work

Compressor work can expressed as

W = h q                                                    (1)

where

W = compression work (Btu min)

h = heat of compression (Btu/lb)

q = refrigerant circulated (lb/min)

### Compression Horsepower

Compression horsepower can be expressed as

P = W / 42.4                                                (2)

where

P = compression power (hp)

W = compression work (Btu min)

Alternatively

P = c / (42.4 COP)                                          (2b)

where

P = compression power (hp)

c = capacity (Btu/min)

COP = coefficient of performance

### Compression horsepower per Ton

p = 4.715 / COP                                             (2c)

where

p = compressor horsepower per Ton (hp/Ton)

COP = coefficient of performance

### COP - Coefficient of Performance

COP = NRE / h                                            (3)

where

COP = Coefficient of Performance

NRE = Net Refrigeration Effect (Btu/lb)

h = heat of compression (Btu/lb)

### Net Refrigeration Effect

Net refrigeration effect can be expressed as

NRE = h l - h e (4)

where

NRE = Net Refrigeration Effect (Btu/lb)

h l = enthalpy of vapor leaving evaporator (Btu/lb)

h e = enthalpy of vapor entering evaporator (Btu/lb)

### Capacity

c = q NRE                                                  (5)

where

c = capacity (Btu/min)

q = refrigerant circulated (lb/min)

NRE = Net Refrigeration Effect (Btu/lb)

### Compressor Displacement

d = c v / NRE                                             (6)

where

d = compressor displacement (ft 3 /min)

c = capacity (Btu/min)

v = volume of gas entering compressor (ft 3 /lb)

NRE = Net Refrigeration Effect (Btu/lb)

### Heat of Compression

h = h lc - h ec (7)

where

h = heat of compression (Btu/lb)

h lc = enthalpy of vapor leaving compressor (Btu/lb)

h ec = enthalpy of vapor entering compressor (Btu/lb)

### Volumetric Efficiency

μ = 100 w a / w t (8)

where

μ = volumetric efficiency

w a = actual weight of refrigerant

w t = theoretical weight of refrigerant

### Compression Ratio

CR = p h / p s (9)

where

CR = compression rate

p h = head pressure absolute (psia)

p s = suction pressure, absolute (psia)

## Related Topics

• ### Air Conditioning

Air Conditioning systems - heating, cooling and dehumidification of indoor air for thermal comfort.

## Related Documents

Calculating chiller and cooling tower refrigeration loads - in tons.
• ### Cooling Load - Convert between kW/ton to COP or EER

Convert between cooling load units like kW/ton, COP and EER.
• ### Cooling Power vs. Airflow and Duct Sizes

Typical relations between cooling power (tons cooling), air flow and duct size
• ### Net Refrigeration Effect

The quantity of heat absorbed from a refrigerated space.
• ### Refrigerants - Environmental Properties

Physical and environmental properties of some common refrigerants.
• ### Refrigeration Machinery - Required Ventilation

Ventilation required for refrigeration machinery and compressors in hot areas.

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## Citation

• The Engineering ToolBox (2010). Refrigeration Formulas. [online] Available at: https://www.engineeringtoolbox.com/refrigeration-formulas-d_1695.html [Accessed Day Month Year].

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