Alveolar Gas Equation Calculator (PAO₂)
Alveolar Gas Equation Calculator (PAO₂)
Calculate alveolar pO₂ from FiO₂, PaCO₂, atmospheric pressure and respiratory quotient — the reference value the A-a gradient is built on.
Alveolar Gas Equation (PAO₂)
4 inputs → PAO2FiO₂ 21%, PaCO₂ 40 mmHg, atmospheric pressure 760 mmHg, RQ 0.8
Formula
- FiO₂
- fraction of inspired oxygen (enter as %, used as a fraction)
- 47
- saturated water vapour pressure at 37°C, mmHg — subtracted because inspired gas is fully humidified by the time it reaches the alveolus
- Patm
- atmospheric pressure, mmHg — 760 at sea level, lower at altitude
- RQ
- respiratory quotient, CO₂ produced ÷ O₂ consumed — 0.8 on a mixed diet, 1.0 on pure carbohydrate, 0.7 on pure fat
Worked example
FiO₂ 21%, PaCO₂ 40 mmHg, atmospheric pressure 760 mmHg, RQ 0.8
(21 ÷ 100) × (760 − 47) = 0.21 × 713 = 149.7
40 ÷ 0.8 = 50.0
149.7 − 50.0 = 99.7 mmHg
What moves PAO₂
| Factor | Effect |
|---|---|
| Higher FiO₂ | Raises PAO₂ directly and substantially |
| Higher PaCO₂ (hypoventilation) | Lowers PAO₂ — CO₂ displaces alveolar oxygen |
| Lower atmospheric pressure (altitude) | Lowers PAO₂ — less total pressure to go around |
| Lower RQ (fat-predominant metabolism) | Raises PAO₂ slightly for the same PaCO₂ |
What the equation isolates
The alveolar gas equation calculates the oxygen tension that should be present in the alveolus given the inspired oxygen fraction, the alveolar (approximated by arterial) CO₂, the ambient pressure and the respiratory quotient. It exists mainly to be compared against the measured arterial pO₂: the difference is the alveolar-arterial (A-a) gradient, which separates hypoxaemia caused by hypoventilation or low inspired oxygen — where PAO₂ itself is low, and the gradient is normal — from hypoxaemia caused by a true gas exchange problem such as shunt, V/Q mismatch or diffusion impairment, where PAO₂ is normal or high but the measured PaO₂ falls well short of it.
Two terms are easy to misread. The 47 mmHg subtracted from atmospheric pressure is the saturated water vapour pressure at body temperature, accounting for the fact that inspired air is fully humidified by the time it reaches the alveolus — it applies regardless of FiO₂ or altitude. The respiratory quotient, defaulted to 0.8 for a mixed diet, rises to 1.0 on a pure carbohydrate load and falls to about 0.7 on a pure fat-based one; it changes the result only modestly across its plausible range.
Altitude enters through atmospheric pressure alone. Denver, at about 1600 m, has a barometric pressure near 630 mmHg rather than 760 — substituting that value into the equation lowers PAO₂ by roughly 27 mmHg before any change in FiO₂ or ventilation, which is why blood gas interpretation at altitude needs an altitude-adjusted reference range.
Frequently asked questions
What is the alveolar gas equation used for?
It calculates the expected alveolar pO₂ so it can be compared with the measured arterial pO₂. The difference — the A-a gradient — separates a low PaO₂ caused by hypoventilation or low inspired oxygen from one caused by a true gas exchange problem.
Why is 47 subtracted from atmospheric pressure?
47 mmHg is the saturated water vapour pressure at 37°C. Inspired gas is fully humidified by the time it reaches the alveolus, so that pressure is no longer available to oxygen and CO₂.
How does altitude affect PAO₂?
Through the fall in atmospheric pressure. At around 1600 m (roughly Denver’s elevation), barometric pressure falls to about 630 mmHg, which alone lowers PAO₂ by roughly 27 mmHg before any other factor changes.
What respiratory quotient should I use?
0.8 is the standard default for a mixed diet. It rises toward 1.0 with a carbohydrate-predominant intake and falls toward 0.7 with a fat-predominant one; the effect on the result is modest.
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References
- Sarkar M, Niranjan N, Banyal PK. Mechanisms of hypoxemia. Lung India. 2017;34(1):47–60.
- West JB. Respiratory Physiology: The Essentials, 10th edition — gas exchange and the alveolar gas equation.