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A–a Gradient Calculator

Find the A–a oxygen gradient.

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.

Try this example →

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.

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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