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A-a Gradient Calculator

Calculate the alveolar-arterial (A-a) oxygen gradient to assess the efficiency of gas exchange and evaluate causes of hypoxemia.

Enter arterial partial pressure of oxygen in mmHg
Enter arterial partial pressure of carbon dioxide in mmHg
Select the fraction of inspired oxygen
Enter patient age in years
Enter atmospheric pressure in mmHg (default: 760 mmHg at sea level)

How to Use This Calculator

  1. Enter the arterial oxygen partial pressure (PaO₂) from ABG results
  2. Enter the arterial carbon dioxide partial pressure (PaCO₂) from ABG results
  3. Select the fraction of inspired oxygen (FiO₂) the patient is receiving
  4. Enter the patient's age to calculate expected A-a gradient
  5. Click Calculate to see the A-a gradient and its interpretation

Formula Used

PAO₂ = (FiO₂ × (Patm - PH₂O)) - (PaCO₂ / RQ)
A-a gradient = PAO₂ - PaO₂

Where:

  • PAO₂ = Alveolar oxygen partial pressure
  • FiO₂ = Fraction of inspired oxygen (0.21 on room air)
  • Patm = Atmospheric pressure (760 mmHg at sea level)
  • PH₂O = Water vapor pressure (47 mmHg at body temperature)
  • PaCO₂ = Arterial carbon dioxide partial pressure
  • RQ = Respiratory quotient (0.8 on a mixed diet)
  • PaO₂ = Arterial oxygen partial pressure

Example Calculation

Real-World Scenario:

A 65-year-old patient on room air has an ABG showing PaO₂ of 80 mmHg and PaCO₂ of 40 mmHg. Calculate the A-a gradient.

Given:

  • PaO₂ = 80 mmHg
  • PaCO₂ = 40 mmHg
  • FiO₂ = 0.21 (room air)
  • Patm = 760 mmHg (sea level)
  • Age = 65 years

Calculation:

PAO₂ = (0.21 × (760 - 47)) - (40 / 0.8) = 149.7 - 50 = 99.7 mmHg

A-a gradient = 99.7 - 80 = 19.7 mmHg

Expected A-a gradient = 4 + (65/4) = 20.25 mmHg

Result: The calculated A-a gradient of 19.7 mmHg is within the expected range for a 65-year-old patient, indicating normal gas exchange.

Why This Calculation Matters

Practical Applications

  • Differentiating causes of hypoxemia (V/Q mismatch vs. shunt)
  • Evaluating severity of pulmonary disease
  • Assessing response to oxygen therapy
  • Diagnosing pulmonary embolism and ARDS

Key Benefits

  • Helps identify the mechanism of hypoxemia
  • Guides further diagnostic workup
  • Assists in treatment decisions
  • Provides objective measure of gas exchange efficiency

Common Mistakes & Tips

A common mistake is using the oxygen flow rate instead of the actual FiO₂. For example, a nasal cannula at 2 L/min delivers approximately 28% FiO₂, not 2%. Use the appropriate FiO₂ value based on the oxygen delivery device and flow rate. When in doubt, measure the actual FiO₂ delivered.

The normal A-a gradient increases with age (approximately 4 mmHg + age/4). A value that might be abnormal in a young adult could be normal in an elderly patient. Always consider the patient's age when interpreting the A-a gradient.

Frequently Asked Questions

An increased A-a gradient indicates a problem with oxygen transfer from alveoli to blood. Common causes include V/Q mismatch (asthma, COPD, pulmonary embolism), shunt (atelectasis, ARDS, pulmonary edema), and diffusion impairment (pulmonary fibrosis). In contrast, hypoventilation and high altitude cause hypoxemia with a normal A-a gradient.

In pulmonary embolism, the A-a gradient is typically increased due to V/Q mismatch. A normal A-a gradient in a patient with dyspnea makes pulmonary embolism less likely, while an increased gradient increases suspicion. However, the A-a gradient alone is not diagnostic and must be interpreted in the clinical context with other tests and findings.

The A-a gradient is the absolute difference between alveolar and arterial oxygen (PAO₂ - PaO₂), while the A-a ratio is the proportion of oxygen that transfers from alveoli to blood (PaO₂/PAO₂). The A-a gradient increases with age, while the A-a ratio typically remains constant with age. The A-a ratio is often preferred in research studies, while the A-a gradient is more commonly used in clinical practice.

References & Disclaimer

Medical Disclaimer

This calculator is for educational and informational purposes only. It should not be used as a substitute for professional medical advice, diagnosis, or treatment. Always seek the advice of a qualified healthcare provider with any questions you may have regarding a medical condition.

References

Accuracy Notice

This calculator uses standard values for water vapor pressure (47 mmHg) and respiratory quotient (0.8). Actual values may vary based on individual patient factors and clinical conditions. The A-a gradient calculation assumes steady-state conditions and may not be accurate in rapidly changing clinical situations.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

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