A-a Gradient Calculator
The alveolar-arterial (A-a) oxygen gradient is the difference between the oxygen in the alveoli and the oxygen measured in arterial blood. It helps determine whether low blood oxygen is due to a gas-exchange problem or simply to hypoventilation or low inspired oxygen. The alveolar oxygen is found with the alveolar gas equation using FiO2, atmospheric pressure, water vapor pressure, PaCO2 and the respiratory quotient. This calculator returns the alveolar oxygen, the A-a gradient and the age-expected value for comparison. Constants are editable for altitude. This is educational, not a diagnosis.
A-a gradient formula
PAO2 = FiO2 * (Patm - PH2O) - (PaCO2 / RQ)
A-a gradient = PAO2 - PaO2
Age-expected = (age / 4) + 4 (room air estimate)
All pressures in mmHg; FiO2 a fraction
At sea level the standard constants are atmospheric pressure 760 mmHg, water vapor 47 mmHg and a respiratory quotient of 0.8. These are editable for altitude or other assumptions.
A-a gradient context
- Normal upper limit on room air roughly equals age/4 plus 4.
- A high gradient suggests a gas-exchange problem.
- A normal gradient with hypoxemia suggests hypoventilation or low inspired oxygen.
- FiO2 is 0.21 on room air and rises with supplemental oxygen.
- Constants change at altitude; edit them as needed.
A-a gradient: frequently asked questions
How is the A-a gradient calculated?
First the alveolar oxygen (PAO2) is found with the alveolar gas equation: PAO2 equals FiO2 times (atmospheric pressure minus water vapor pressure) minus PaCO2 divided by the respiratory quotient. The A-a gradient is then PAO2 minus the measured arterial oxygen (PaO2).
What values are standard for the constants?
At sea level, atmospheric pressure is about 760 mmHg and water vapor pressure at body temperature is about 47 mmHg. The respiratory quotient is usually taken as 0.8. All three are editable here for altitude or different assumptions.
What is a normal A-a gradient?
On room air a rough normal upper limit is age divided by 4, plus 4, in mmHg. This calculator shows that age-expected value for comparison. A gradient above the expected value suggests a problem with gas exchange.
What does a high A-a gradient indicate?
An elevated gradient points to causes such as ventilation-perfusion mismatch, shunt or diffusion impairment, rather than pure hypoventilation. A normal gradient with low oxygen suggests hypoventilation or low inspired oxygen. Interpretation is clinical.
Is this a diagnosis?
No. The A-a gradient is one physiologic measure. It must be interpreted with the clinical picture by a qualified clinician. This calculator is for education only.
Official sources
- National Heart, Lung, and Blood Institute: Oxygen and respiratory physiology.
- National Library of Medicine (NCBI): Alveolar gas equation literature.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.