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Alveolar Gas Equation Calculator

Find alveolar oxygen pressure and the A–a gradient.

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.

Worked example

Room air at 760 mmHg with FiO2 0.21, PaCO2 40, R 0.8 and measured PaO2 90. First the dry-gas pressure: 760 − 47 = 713 mmHg, and 0.21 × 713 = 149.73. The carbon dioxide term is 40 ÷ 0.8 = 50. So PAO2 = 149.73 − 50 = 99.73. The A–a gradient is 99.73 − 90 = 9.73 mmHg.

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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 simply gives a negative number, usually a sign of a wrong input.

Sources

About this calculator

The alveolar gas equation — PAO2 = FiO2 × (Patm − PH2O) − (PaCO2 / R) — calculates the partial pressure of oxygen inside the alveoli. Combined with a measured arterial PaO2, it produces the A–a gradient, a key diagnostic value in pulmonology and critical care for assessing how well oxygen is diffusing from the lungs into the blood.

Physicians, respiratory therapists and medical students use it to distinguish the causes of low blood oxygen: the A–a gradient stays normal when hypoxemia is caused by simple hypoventilation, but rises when the real problem is a ventilation-perfusion mismatch, a shunt, or a diffusion defect.

Atmospheric pressure has to be the local value in mmHg at altitude, since altitude itself is not a separate input.

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