Alveolar Gas Equation Calculator

How it is calculated

The tool applies the alveolar gas equation with water vapour pressure fixed at 47 mmHg (body temperature): PAO2 = FiO2 × (Patm − 47) − PaCO2 ÷ R. FiO₂ is the inspired oxygen fraction as a decimal above 0 and up to 1 (0.21 for room air), Patm is barometric pressure in mmHg, PaCO₂ is arterial carbon dioxide in mmHg and R is the respiratory quotient. The A–a gradient is PAO2 − PaO2 using the measured arterial PaO₂ (mmHg). All five fields are required, with no defaults and no altitude input. Patm must be above 47 and at most 4000, PaO₂ at most 800, and a combination that would make PAO₂ negative gives no result. Results are in mmHg, shown without a unit.

Common mistakes

• Entering FiO₂ as a percentage. The field takes a fraction, so room air is 0.21; typing 21 returns no result because anything above 1 is rejected.
• Using sea-level pressure at altitude. There is no altitude field, so the actual local barometric pressure must be typed in mmHg, not kPa.
• Leaving out the respiratory quotient. It has no default, so a value like 0.8 must be supplied; a very small R makes the CO₂ term huge and can push PAO₂ below zero, which gives no result.
• Entering PaO₂ from a venous sample or a pulse-oximeter saturation. The gradient needs arterial PaO₂ in mmHg, not a percentage.
• Reading the gradient as an abnormal value whenever it looks odd. The tool shows the raw difference and applies no age-adjusted normal range; a measured PaO₂ above the calculated PAO₂ (110 here) simply gives a negative number, usually a sign of a wrong input.