Alveolar–Arterial (A–a) Oxygen Gradient: Localising the Cause of Hypoxaemia

What it is

The alveolar–arterial (A–a) oxygen gradient is the difference between the oxygen tension calculated in the alveolus (PAO₂) and the oxygen tension actually measured in arterial blood (PaO₂). It is the single most useful bedside number for answering one question: why is this patient hypoxaemic? A normal gradient with low PaO₂ implicates hypoventilation or a low inspired oxygen fraction; a widened gradient implicates a problem at the gas-exchange interface — V/Q mismatch, right-to-left shunt, or a diffusion defect.

The method

First compute alveolar oxygen tension with the alveolar gas equation:

PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / 0.8

• 47 mmHg is the saturated water-vapour pressure at 37 °C.
• Patm defaults to 760 mmHg at sea level (drop it at altitude).
• 0.8 is the assumed respiratory quotient.

Then:

A–a gradient = PAO₂ − PaO₂

When to use it

Reach for the A–a gradient whenever you have an arterial gas and need to characterise hypoxaemia — undifferentiated respiratory distress, suspected pulmonary embolism, evaluating a sedated patient who is hypoxaemic, or distinguishing a primary lung problem from pure hypoventilation (e.g. opioid effect, neuromuscular weakness). A normal gradient with a high PaCO₂ points firmly at hypoventilation; a wide gradient says the lung itself is the problem.

Worked example

A child on room air (FiO₂ 0.21) with PaCO₂ 40 mmHg and PaO₂ 70 mmHg at sea level:

• PAO₂ = 0.21 × (760 − 47) − 40 / 0.8 = 0.21 × 713 − 50 = 149.7 − 50 = 99.7 mmHg
• A–a gradient = 99.7 − 70 = ≈30 mmHg

That is a widened gradient (a healthy young patient on room air sits well under ~15 mmHg), so the hypoxaemia reflects a gas-exchange defect, not hypoventilation.

Pitfalls and caveats

• Enter FiO₂ as a fraction (0.21, not 21) in the alveolar gas equation.
• The gradient widens normally with higher FiO₂ — it is most interpretable on room air. A “high” gradient on 100% oxygen is expected and far less informative.
• The age-based normal (roughly age/4 + 4 mmHg in adults) is small in children; do not apply adult thresholds blindly to a neonate or infant.
• The respiratory quotient of 0.8 is an assumption; it shifts with diet and metabolic state.
• At altitude, substitute the true atmospheric pressure or the alveolar maths overstates PAO₂.

Run it: Alveolar–Arterial (A–a) Oxygen Gradient

Decision support for qualified clinicians only — verify against current primary guidelines and your clinical judgement.