# Alveolar air equation

The alveolar air equation is the method for calculating partial pressure of alveolar gas (PAO2). The equation is used in assessing if the lungs are properly transferring oxygen into the blood. The alveolar air equation is not widely used in clinical medicine, probably because of the complicated appearance of its classic forms.

## Interpretation

To clinically interpret PaO2 one has to also know the patient's PaCO2, FIO2 (fraction of inspired oxygen) and the PB (barometric pressure), all components of the equation for PAO2.

## Equations

Several possible equations exist to calculate the alveolar air.

{\begin{aligned}P_{A}{\ce {O2}}&=F_{I}{\ce {O2}}\left(PB-P{\ce {H2O}}\right)-P_{A}C{\ce {O2}}\left(F_{I}{\ce {O2}}+{\frac {1-F_{I}{\ce {O2}}}{R}}\right)\\&=P_{I}{\ce {O2}}-P_{A}C{\ce {O2}}\left(F_{I}{\ce {O2}}+{\frac {1-F_{I}{\ce {O2}}}{R}}\right)\\&=P_{I}{\ce {O2}}-{\frac {V_{T}}{V_{T}-V_{D}}}\left(P_{I}{\ce {O2}}-P_{E}{\ce {O2}}\right)\\&={\frac {P_{E}{\ce {O2}}-P_{I}{\ce {O2}}\left({\frac {V_{D}}{V_{T}}}\right)}{1-{\frac {V_{D}}{V_{T}}}}}\end{aligned}} ### Abbreviated alveolar air equation

$P_{A}{\ce {O2}}={\frac {P_{E}{\ce {O2}}-P_{i}{\ce {O2}}{\frac {V_{D}}{V_{T}}}}{1-{\frac {V_{D}}{V_{T}}}}}$ PAO2, PEO2, and PiO2 are the partial pressures of oxygen in alveolar, expired, and inspired gas, respectively, and VD/VT is the ratio of physiologic dead space over tidal volume.

### Respiratory quotient (R)

$R={\frac {P_{E}{\ce {CO2}}(1-F_{I}{\ce {O2}})}{P_{i}{\ce {O2}}-P_{E}{\ce {O2}}-(P_{E}{\ce {CO2}}*F_{i}{\ce {O2}})}}$ ### Physiologic dead space over tidal volume (VD/VT)

${\frac {V_{D}}{V_{T}}}={\frac {P_{a}{\ce {CO2}}-P_{E}{\ce {CO2}}}{P_{a}{\ce {CO2}}}}$ 