A-a Gradient Calculator
Work out the alveolar-arterial (A-a) oxygen gradient — the difference between the oxygen in the alveoli and the oxygen in the arterial blood — to help work out why someone is hypoxaemic. A raised gradient points to a problem in the lung itself (such as pulmonary embolism, pneumonia or oedema), while a normal gradient points to hypoventilation or a low inspired oxygen. Enter the arterial blood-gas values, the inspired oxygen and age.
About the A-a gradient
The alveolar-arterial oxygen gradient separates the causes of hypoxaemia into lung problems (raised gradient) and hypoventilation or low inspired oxygen (normal gradient). It is derived from the alveolar gas equation and interpreted against an age-adjusted normal.
Frequently asked questions
How is the A-a gradient calculated?
To calculate the A-a gradient, first the alveolar oxygen is estimated with the alveolar gas equation: PAO₂ = FiO₂ × (atmospheric pressure − water vapour pressure) − PaCO₂ ÷ 0.8, which at sea level on room air is 0.21 × (760 − 47) − PaCO₂ ÷ 0.8. The A-a gradient is then PAO₂ − PaO₂. The 0.8 is the respiratory quotient. This calculator uses a sea-level atmospheric pressure of 760 mmHg.
What is a normal A-a gradient?
The normal gradient rises with age. A common estimate of the upper limit is age ÷ 4 + 4 mmHg (a similar rule is 2.5 + 0.21 × age). So a healthy 20-year-old might have a gradient under about 9 mmHg and a 70-year-old under about 21. Breathing supplemental oxygen widens the normal gradient, so the age rule applies best on room air.
What does a raised gradient mean?
A gradient above the age-expected value indicates that the hypoxaemia comes from the lung — a ventilation/perfusion mismatch, a right-to-left shunt or a diffusion problem, as in pulmonary embolism, pneumonia, pulmonary oedema or interstitial lung disease. A normal gradient with a low PaO₂ points instead to hypoventilation (for example opioid overdose) or a low inspired oxygen, such as at altitude. Supplemental oxygen helps separate the lung causes: hypoxaemia driven by ventilation/perfusion mismatch improves substantially with added oxygen, whereas a true right-to-left shunt responds poorly. This calculator compares your result against the age-expected upper limit of age ÷ 4 + 4 mmHg and labels anything above it as raised.
Does the inspired oxygen matter?
The inspired oxygen fraction changes the result directly, so it is one of the four required inputs. The FiO₂ (fraction of inspired oxygen) is 21% on room air and higher on supplemental oxygen; enter it as a percentage. On high inspired-oxygen concentrations the alveolar oxygen — and therefore the calculated gradient — rises, and the simple age-based normal no longer holds, so the gradient is most useful on room air.
What are typical units?
For the A-a gradient, PaO₂ and PaCO₂ are entered in mmHg, as reported on most arterial blood-gas printouts. If your gas reports in kilopascals (kPa), multiply by 7.5 to convert to mmHg (so a PaO₂ of 10 kPa is 75 mmHg). This calculator is an educational reference, not medical advice.
This is a reference tool, not a diagnosis or medical advice. Results depend on the laboratory, assay and clinical context, and reference intervals vary between labs and by age and sex — always read your result against the range printed on your own report and discuss it with a qualified healthcare professional.
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