For healthcare professionals
A-a Gradient Calculator
The alveolar-arterial (A-a) oxygen gradient is the difference between the oxygen pressure in the alveoli, estimated from the alveolar gas equation, and the oxygen pressure measured in arterial blood. It rises with ventilation-perfusion mismatch or shunting. This tool works on room air at sea level and is written for clinicians; it is not a diagnosis.
Arterial blood gas on room air
Use an arterial blood gas taken while breathing room air at or near sea level. Nothing you enter leaves this page.
What you will see
The A-a gradient with the working, and how it compares with the expected value for age.
Educational only, not medical advice. Not a diagnosis. Decisions belong to the treating team.
Source
The room-air, sea-level formula and the expected value for age as printed by Dhont S and colleagues, Respiratory Research 2020, an open-access (CC BY) review. The tests check the formula, the expected value, that a gradient equal to the expected value is not called raised, and that two different values are never shown as the same number.
Validated in
A physiological formula, not a validated score. The expected value for age applies to adults.
Limits
This version holds only on room air at sea level: it uses a fixed alveolar term of 150 mm Hg. On supplemental oxygen the expected gradient is higher; Dhont 2020 adds 50 x (FiO2 - 0.21) mm Hg to the expected value, but this tool does not calculate the gradient on oxygen. It needs an arterial blood gas; pulse oximetry is not enough.
The formulas
- A-a gradient (mm Hg) = 150 - PaCO2 / 0.8 - PaO2, on room air at sea level (Dhont 2020).
- Expected A-a gradient for age (mm Hg) = age / 4 + 4 on room air, plus 50 x (FiO2 - 0.21) on supplemental oxygen (Dhont 2020).
Worked example: a 40-year-old with a PaO2 of 60 mm Hg and a PaCO2 of 32 mm Hg has a gradient of 150 - 32/0.8 - 60 = 150 - 40 - 60 = 50 mm Hg. The expected value is 40/4 + 4 = 14 mm Hg, so the gradient is raised.
What a raised gradient means
The A-a gradient is increased by ventilation-perfusion (V/Q) mismatch or by intrapulmonary shunting. Hypoxemia from V/Q mismatch can usually be corrected with supplemental oxygen, whereas a shunt responds poorly to oxygen (Dhont 2020). Pure diffusion defects are rarely a cause of a raised gradient at rest (Dhont 2020). The review also notes that pulse oximetry should be read alongside breathing rate and, where possible, an arterial PaO2 (Dhont 2020).
Related tools
On high-flow nasal oxygen, the ROX index calculator compares SpO2/FiO2 and breathing rate with published cut-offs. For ventilated patients, the PaO2/FiO2 ratio calculator gives the Berlin ARDS oxygenation band. For community-acquired pneumonia, the Pneumonia Severity Index includes PaO2 under 60 mm Hg as one item, and the CURB-65 calculator is a shorter severity score. For a metabolic acidosis on the same blood gas, the Winters formula calculator gives the expected PaCO2. Other bedside scores are listed under For healthcare professionals.
Sources
- Dhont S, Derom E, Van Braeckel E, Depuydt P, Lambrecht BN. The pathophysiology of 'happy' hypoxemia in COVID-19. Respir Res. 2020;21:198. doi:10.1186/s12931-020-01462-5. PMID 32723327. Open access (CC BY). Text (P(A-a)O2 = 150 - PaCO2/0.8 - PaO2 at sea level; expected age/4 + 4 + 50 x (FiO2 - 0.21); V/Q mismatch and shunt; diffusion defects rarely raise it at rest). pmc.ncbi.nlm.nih.gov/articles/PMC7385717/
Written and maintained by the uncovermyrisk.com editorial team. We do not have a medical reviewer; every claim links to its primary source above. Last reviewed: 2026-11-02. Spotted an error? See About.