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A–a Gradient & Alveolar Gas Equation

Alveolar oxygen (PAO₂) by the alveolar gas equation and the alveolar–arterial gradient.

For healthcare professionalsRespiratoryv1.0.1

For healthcare professionals / clinical use. Not a self-diagnosis tool.

Your measurements

%
years
mmHg

Calculated on your device. Nothing is sent to a server.

Your result will appear here

Enter your measurements, then press Calculate.

Methodology

Alveolar gas equation; Mellemgaard age norm

PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ ÷ 0.8; A–a = PAO₂ − PaO₂; a commonly used age-based approximation of the normal gradient is 2.5 + 0.21 × age mmHg, commonly attributed to Mellemgaard (1966)

Assumes a respiratory quotient of 0.8 and water vapour pressure of 47 mmHg at 37 °C.

Who it is for
Adults with an arterial blood gas.
Version
1.0.1

How this calculator works

Where the formula comes from

  • The alveolar gas equation estimates alveolar oxygen pressure, which cannot be sampled directly: PAO₂ = FiO₂ × (Patm − PH₂O) − PaCO₂ ÷ RQ, with Patm 760 mmHg at sea level.[1]
  • Mellemgaard (1966) studied the size and components of the alveolar–arterial oxygen difference in healthy people.[2]

The inputs

  • At sea level on room air with PaCO₂ 40 mmHg, PAO₂ = (760 − 47) × 0.21 − 40 ÷ 0.8 ≈ 99.7 mmHg.[1]

Where accuracy falls (published evidence)

  • The respiratory quotient varies with diet and metabolic state (about 0.82 on an average diet); 0.8 is an assumption.[1]

Sources

  1. Hendrix JM, Burns B. Alveolar Gas Equation. In: StatPearls. Treasure Island (FL): StatPearls Publishing; 2024. PMID 29489223
  2. Mellemgaard K. The alveolar-arterial oxygen difference: its size and components in normal man. Acta Physiol Scand. 1966;67(1):10–20. doi:10.1111/j.1748-1716.1966.tb03281.x

Compiled from the published sources above. Every statement was agreed independently by three AI research tools (Claude, ChatGPT, DeepSeek) and its source verified in PubMed or Crossref by the Hakeemly editorial team. Not reviewed by a doctor unless stated. Agreed on

Worked example: how to calculate A–a gradient

Inputs

FiO₂ (inspired oxygen)
21 %
PaO₂ (arterial oxygen)
90 mmHg
PaCO₂
40 mmHg
Age
40 years

Result

A–a gradient
10 mmHg
Alveolar PAO₂
100 mmHg
Approximate upper normal for age
11 mmHg

An illustration with sample values, worked out with the same method the tool above uses.

Limitations

  • RQ varies with diet and illness; interpret with the clinical picture.

References

  1. West JB, Luks AM. West's Respiratory Physiology: The Essentials. 11th ed. Philadelphia: Wolters Kluwer; 2021.
  2. Mellemgaard K. The alveolar-arterial oxygen difference: its size and components in normal man. Acta Physiol Scand. 1966;67(1):10–20. doi:10.1111/j.1748-1716.1966.tb03281.x
  3. Hendrix JM, Burns B. Alveolar Gas Equation. In: StatPearls. Treasure Island (FL): StatPearls Publishing; 2024. https://www.ncbi.nlm.nih.gov/books/NBK482268/

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