The compression ratio expresses how much the working air has been compressed relative to free air at atmospheric conditions. Multiplying the cylinder intake volume (cfm) by this ratio converts to the free-air equivalent (scfm) that the compressor must supply.

\begin{equation}\label{eq:pneumatic-air-requirement-compression-ratio} r_c = \frac{P_{gauge} + P_{atm}}{P_{atm}} \end{equation}

Symbols

\(r_c\)	Compression ratio (absolute working pressure / atmospheric pressure) \([\unit{ \unitless}]\)
\(P_{gauge}\)	Operating gauge pressure at the cylinder inlet \([\unit{ \psi}]\)
\(P_{atm}\)	Atmospheric pressure (14.7 psia at sea level) \([\unit{ \psi}]\)

Note: \(P_{atm} = 14.7\) psia at sea level (see physics::us::kAtmosphericPressurePsi). At higher elevations the actual atmospheric pressure is lower, which increases the compression ratio and the air consumption. This formula assumes sea-level conditions.