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# Horsepower required to Compress Air

## Calculate horsepower required by air compressors.

The horsepower required to adiabatic compression of air can be calculated with the calculator below:

N - number of stages

V - volume flow of compressed air at atmospheric pressure (cfm, ft3/min)

P2 - absolute final pressure (psi)

Theoretical horsepower required to compress one cubic foot of free air (atmospheric pressure) for single-staged, two-staged and three-staged compressors are indicated in the diagram below. In general - plus 15-20%  friction.

• 1 cfm (ft3/min) = 1.7 m3/h = 0.47 l/s = 28.3 l/min
• 1 psi (lb/in2) = 6894.8 Pa (N/m2) =  6.895 10-2 bar
• 1 hp = 745.7 W

The power required for adiabatic (process without transfer of heat) compression of air can be expressed as

HP = [144 N P1 V k / (33000 (k - 1))] [(P2 / P1)(k - 1)/N k - 1]                                (1)

where

HP = horsepower

N = number of compression stages

k = 1.41 = adiabatic expansion coefficient

P1 = absolute initial atmospheric pressure (psi) (14.7 psi at sea level)

P2 = absolute final pressure after compression (psi)

V = volume of air at atmospheric pressure - standard or free air (scfm, ft3/min)

• adiabatic compression (or expansion) takes place without transmission of heat

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Temperature

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Length

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yards
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naut miles

Area

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Volume

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Weight

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Velocity

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Pressure

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mm H2O
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psi
inches H2O

Flow

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US gpm
cfm

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