A-a Gradient Calculator
A-a Gradient Calculator
Calculate the alveolar-arterial oxygen gradient to distinguish hypoxaemia from V/Q mismatch or shunt from hypoxaemia caused by hypoventilation alone.
A-a Gradient
Oxygenation defectFiO₂ 21%, PaCO₂ 40 mmHg, PaO₂ 70 mmHg, age 60, Patm 760 mmHg
Formula
- 47
- water vapour pressure in the airway at 37°C, mmHg
- 0.8
- the respiratory quotient, converting CO₂ produced to O₂ consumed
- Patm
- atmospheric pressure, mmHg — 760 at sea level; lower at altitude
- expected gradient
- rises with age, approximately (age ÷ 4) + 4 mmHg
Worked example
FiO₂ 21%, PaCO₂ 40 mmHg, PaO₂ 70 mmHg, age 60, Patm 760 mmHg
PAO₂ = 0.21 × (760 − 47) − 40 ÷ 0.8 = 0.21 × 713 − 50 = 149.7 − 50 = 99.7 mmHg
A–a gradient = 99.7 − 70 = 29.7 mmHg
Expected for age 60 ≈ 60 ÷ 4 + 4 = 19 mmHg, so this result is modestly raised for age
Interpreting a raised or normal gradient
| Finding | Likely mechanism |
|---|---|
| Raised gradient + hypoxaemia | V/Q mismatch, shunt, or diffusion impairment |
| Normal gradient + hypoxaemia | Hypoventilation, or low inspired oxygen (e.g. altitude) |
What the gradient separates, and its limits
The alveolar-arterial gradient compares the oxygen the alveolus should contain, calculated from the alveolar gas equation, against the oxygen actually measured in arterial blood. The alveolar side is PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ ÷ 0.8, where 47 mmHg is the water vapour pressure of fully humidified air at body temperature and 0.8 is the respiratory quotient, which converts CO₂ eliminated back into an equivalent oxygen term.
The gradient’s value is in what it separates. Pure hypoventilation lowers PaO₂ but lowers the calculated PAO₂ by the same amount, so the gradient stays normal — this is the signature of opioid overdose, neuromuscular weakness, or severe obesity hypoventilation. A raised gradient means the alveolar oxygen is present but is not reaching arterial blood, which points to V/Q mismatch, right-to-left shunt, or a diffusion barrier — pulmonary embolism, pneumonia, pulmonary oedema, or interstitial lung disease. The same logic applies to low inspired oxygen at altitude: PAO₂ falls, PaO₂ falls with it, and the gradient again stays normal despite significant hypoxaemia.
The expected gradient is not a fixed number. It widens with age, roughly by age ÷ 4 plus 4 mmHg, so a gradient of 20 mmHg is clearly abnormal at age 20 but unremarkable at 65. The equation also assumes standard sea-level conditions; the atmospheric pressure input here lets it be applied correctly at altitude, where a lower Patm lowers the calculated alveolar oxygen and, without adjustment, would be misread as disease.
Frequently asked questions
What does the A-a gradient tell you?
Whether hypoxaemia is caused by a problem getting oxygen from alveolus to blood (V/Q mismatch, shunt, diffusion impairment — raised gradient) or by reduced ventilation or low inspired oxygen alone (normal gradient).
Why does the expected gradient depend on age?
The normal gradient widens with age, approximately by (age ÷ 4) + 4 mmHg, reflecting the gradual, physiological decline in ventilation-perfusion matching over a lifetime.
Does the A-a gradient work at altitude?
Only if the atmospheric pressure is adjusted for the altitude — the standard equation assumes sea level (760 mmHg). Using a lower atmospheric pressure lowers the calculated alveolar oxygen and keeps the gradient accurate.
Can the A-a gradient be normal despite significant hypoxaemia?
Yes. In pure hypoventilation or at low inspired oxygen, PaO₂ falls but the calculated alveolar oxygen falls with it, so the gradient stays normal even though the patient is clearly hypoxaemic.
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References
- Story DA. Alveolar oxygen partial pressure, alveolar carbon dioxide partial pressure, and the alveolar gas equation. Anesthesiology. 2013;119(3):499–500.
- West JB, Luks AM. West’s Respiratory Physiology: The Essentials, 11th ed. Wolters Kluwer, 2020.