Alveolar-Arterial (A-a) Gradient Calculator
The A-a gradient (alveolar-arterial gradient) measures the difference between alveolar oxygen concentration (PAO2) and arterial oxygen concentration (PaO2), helping differentiate between hypoventilation and intrinsic lung pathology as causes of hypoxemia.
About
The A-a gradient is calculated using the alveolar gas equation: PAO2 = (FiO2 × (Patm − PH2O)) − (PaCO2 / RQ), where Patm is atmospheric pressure (760 mmHg at sea level), PH2O is water vapor pressure (47 mmHg at 37°C), and RQ is the respiratory quotient (0.8). The normal A-a gradient is 5-20 mmHg on room air and increases with age. An elevated gradient indicates V/Q mismatch, shunt, or diffusion impairment. A normal gradient with hypoxemia suggests hypoventilation.
Formula
PAO2 = (FiO2 × (Patm − 47)) − (PaCO2 / 0.8); A-a Gradient = PAO2 − PaO2; Expected A-a = (Age/4) + 4
The alveolar gas equation calculates PAO2 using the inspired FiO2, barometric pressure minus water vapor (47 mmHg), and the ratio of PaCO2 to the respiratory quotient (0.8). The A-a gradient is the difference between this calculated alveolar PO2 and the measured arterial PO2.
Score Interpretation
The A-a gradient is essential for differentiating causes of hypoxemia. A normal gradient with hypoxemia indicates hypoventilation (e.g., opioid overdose, neuromuscular disease). An elevated gradient indicates V/Q mismatch (e.g., COPD, asthma), shunt (e.g., ARDS, pneumonia), or diffusion impairment (e.g., ILD, pulmonary fibrosis). The gradient increases with age and is affected by FiO2 and altitude.
A-a Gradient Result — 0+
Interpret visually based on age-adjusted expected gradient.
Management: Interpret in clinical context.
Reference Ranges
| Population | Normal Range | Notes |
|---|---|---|
| Young adults (room air) | 5-15 mmHg | Increases by 4 mmHg per decade of life |
Dr. Khaled Hassan
Dr. Khaled is a cardiology consultant with experience in acute cardiac care.
View medical review board & editorial policy →Example Calculation
A 65-year-old patient on room air (FiO2 0.21) has PaO2 55 mmHg, PaCO2 40 mmHg. PAO2 = (0.21 × (760−47)) − (40/0.8) = 149.73 − 50 = 99.73. A-a gradient = 99.73 − 55 = 44.73 mmHg. Expected = (65/4) + 4 = 20.25. Elevated gradient indicates V/Q mismatch or shunt.
Related Conditions
Common Mistakes
Forgetting to account for FiO2 when interpreting A-a gradient
Always use the actual FiO2. On room air FiO2 is 0.21, but on supplemental oxygen, FiO2 may be much higher.
Frequently Asked Questions
What is a normal A-a gradient?
What causes an elevated A-a gradient?
References
- Martin L. All you really need to know to interpret arterial blood gases. 2nd ed. Lippincott Williams & Wilkins; 1999.
- Williams AJ. ABC of oxygen: assessing and interpreting arterial blood gases. BMJ. 1998;317(7167):1213-1216. PubMed