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A–a Gradient Calculator

Find the A–a oxygen gradient.

Result

9.73 mmHg
99.73 mmHg

How it is calculated

The tool first estimates the oxygen pressure in the alveoli with the alveolar gas equation: PAO₂ = FiO₂ × (760 − 47) − PaCO₂ / 0.8. It uses a fixed barometric pressure of 760 mmHg, water vapour pressure of 47 mmHg (so 713 mmHg of dry gas) and a respiratory quotient of 0.8. The gradient is then A–a = PAO₂ − PaO₂.

FiO₂ is entered as a fraction between 0 and 1 (0.21 for room air), and PaCO₂ and PaO₂ in mmHg from an arterial blood gas. Both pressures must be zero or more. The fixed sea-level pressure means results at altitude are not corrected. This is a calculation aid, not a diagnosis, and a clinician has to interpret it with the whole clinical picture.

Worked example

Room air (FiO₂ 0.21), PaCO₂ 40 mmHg, PaO₂ 90 mmHg. Alveolar oxygen: 0.21 × 713 = 149.73, minus 40 / 0.8 = 50, gives 99.73 mmHg. The A–a gradient is 99.73 − 90 = 9.73 mmHg.

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Common mistakes

  • Typing FiO₂ as a percentage (21) instead of a fraction (0.21); the tool then returns no result.
  • Using venous or capillary values instead of arterial ones, which gives a PaO₂ that is not comparable.
  • Applying the same normal limit at every age and every FiO₂. The expected gradient rises with age and with higher oxygen delivery, so compare against the right reference.
  • Forgetting that the tool assumes sea-level pressure, which misleads at high altitude.

Sources

About this calculator

The alveolar–arterial (A–a) gradient measures the difference between the oxygen concentration in the alveoli (PAO₂, calculated from the alveolar gas equation using FiO₂, atmospheric pressure, and PaCO₂) and the oxygen actually measured in arterial blood (PaO₂ from an arterial blood gas): A–a gradient = PAO₂ − PaO₂.

A normal gradient (roughly 5–15 mmHg, increasing with age) means any low blood oxygen is due to a problem getting air into the lungs, like hypoventilation; an elevated gradient points to a problem with gas exchange itself — ventilation-perfusion mismatch, shunt, or diffusion impairment — as seen in pulmonary embolism, pneumonia, pulmonary edema, or ARDS.

Emergency and critical care physicians assessing a patient's respiratory failure, pulmonologists working up hypoxemia, and medical and nursing students learning arterial blood gas interpretation all use this calculation to narrow down the cause of low oxygen.

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Comments (1)

  • Editorial team

    The tool also shows the alveolar oxygen it calculated, which helps when checking a hand calculation line by line. A rule of thumb often taught for the upper limit on room air is age ÷ 4 + 4, so about 19 mmHg at 60, but the gradient widens on higher FiO₂ and the fixed 760 mmHg ignores altitude. Interpretation belongs with a clinician. Which reference limit does your course or unit use?

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