Inspired oxygen minus carbon dioxide divided by the respiratory quotient
Mnemonic
“Alveolar oxygen is what you breathe in, minus what carbon dioxide displaces”:
PAO2 = FiO2 x (Patm - PH2O) - PaCO2 / R
In kPa on air at sea level: PAO2 = 0.21 x (101 - 6.3) - PaCO2 / 0.8, giving roughly 20 - 1.25 x PaCO2.
- Patm - PH2O accounts for humidification in the airway, and water vapour pressure at body temperature is a constant 6.3 kPa (47 mmHg)
- R is the respiratory quotient, normally 0.8
The equation exists to calculate the A-a gradient, which is the whole point: normal is under 2 kPa, rising with age to roughly age/4 + 4 in mmHg.
A normal gradient with hypoxia means hypoventilation or low inspired oxygen; a raised gradient means a gas exchange problem (shunt, V/Q mismatch or diffusion impairment). That single division is the most useful thing the equation does.
Expansion
PAO2 = FiO2 x (Patm - PH2O) - (PaCO2 / R)
Where the respiratory quotient R is about 0.8.
Breathing air at sea level:
- 0.21 x (101 - 6.3) = 19.9 kPa
- minus 5.3 / 0.8 = 6.6 kPa
- PAO2 = about 13.3 kPa (100 mmHg)
The equation makes three things explicit:
- Rising carbon dioxide displaces oxygen from the alveolus, so hypoventilation alone causes hypoxaemia
- Altitude reduces barometric pressure and therefore alveolar oxygen
- Water vapour occupies a fixed 6.3 kPa (47 mmHg) once gas is fully humidified, which is a larger proportional loss at altitude
Its main clinical use is calculating the alveolar-arterial gradient, which separates hypoxaemia caused by hypoventilation, where the gradient is normal, from hypoxaemia caused by lung disease, where it is widened.