A-a Gradient Calculator With Age-Adjusted Normal Range
Enter an ABG and get the alveolar-arterial oxygen gradient, the age-adjusted expected value, the P/F ratio, and which of the five causes of hypoxemia you are probably looking at.
The formula
PAO2 = FiO2 × (Pbaro − 47) − (PaCO2 ÷ R)
A-a gradient = PAO2 − PaO2
Expected normal (room air) = (age ÷ 4) + 4
PAO2 is the oxygen tension the alveolus should contain, computed from the inspired oxygen after subtracting water vapor pressure (47 mmHg at body temperature) and the CO2 that displaces oxygen, scaled by the respiratory quotient. The gradient is the gap between that ideal and what actually made it into the artery. A widening gap means the lung itself is failing to transfer oxygen. The expected value rises with age because even healthy lungs lose matching efficiency over the decades.
The five causes of hypoxemia, sorted by the gradient
Every hypoxemic patient has one or more of exactly five mechanisms. The A-a gradient sorts them into two piles for you.
Hypoventilation (opioids, CNS depression, neuromuscular weakness): the alveolus has less oxygen because CO2 took its place, but transfer is fine. The PaCO2 is elevated. Low inspired oxygen (altitude): everything works, there is simply less oxygen coming in.
V/Q mismatch (pneumonia, pulmonary edema, PE, COPD): the workhorse cause, and it corrects substantially with supplemental oxygen. Shunt (severe ARDS, intracardiac shunt, complete lobar collapse): blood bypasses ventilated lung entirely, and the defining feature is that oxygen does not fix it. Diffusion limitation (interstitial lung disease): the membrane is thickened; classically worse with exertion.
Put the patient on high-flow oxygen and repeat the gas. V/Q mismatch improves substantially because even poorly ventilated units eventually fill with oxygen. A true shunt barely moves, because the blood causing the problem never meets gas at all. A patient who stays profoundly hypoxemic on 100 percent oxygen has a shunt until proven otherwise.
The gradient pairs naturally with the rest of the gas: interpret the pH and CO2 side with the ABG interpreter, and if the patient is ventilated, translate the numbers into vent changes with the ventilator settings guide. The P/F ratio this calculator reports is the same one used to grade ARDS severity, which matters when you are deciding between escalating oxygen and calling for ECMO-level support. For the full oxygenation workup at the bedside, the night calls guide covers the hypoxemia call step by step.
The formula assumes the FiO2 you enter is the FiO2 the patient is actually receiving, which is only reliably true on room air or a ventilator. A nasal cannula's true FiO2 varies with breathing pattern. Institutional protocol and current references govern clinical decisions.
This is not medical advice. This calculator is an educational tool. Verify every result and every clinical decision against current references and your institution's protocols.