A-a Gradient Calculator (Alveolar-Arterial Oxygen Gradient)

How it works

PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / 0.8; A-a gradient = PAO₂ − PaO₂; normal ≈ age/4 + 4 mmHg on room air

The alveolar gas equation estimates the oxygen tension in the alveoli from the inspired fraction, barometric pressure (less 47 mmHg of water vapour) and the carbon dioxide displacing it. Comparing that to the measured arterial PaO₂ gives the A-a gradient — the “cost” of moving oxygen across the lung. A low PaO₂ with a normal gradient means the alveoli themselves have little oxygen: the patient is hypoventilating (note the high PaCO₂) or breathing thin air. A widened gradient points to a problem in the lung — mismatched ventilation and perfusion, true shunt through unventilated or collapsed lung, or thickened alveolar membranes. The normal gradient rises with age, hence the rule of thumb age/4 + 4. On supplemental oxygen the gradient inflates (5–7 mmHg per 10% FiO₂), so the a/A ratio or P/F ratio is more reliable.

Worked example

PaO₂ 62, PaCO₂ 38 on room air at sea level, age 58: PAO₂ = 0.21 × 713 − 38/0.8 = 102; gradient 40 mmHg versus a normal of about 19 — widened, pointing to V/Q mismatch or shunt.

Frequently asked questions