The alveolar gas equation and the A–a gradient !
- Measurement
- Exam priority: high
A formula estimates how much oxygen is in the alveoli. If arterial blood has much less, the problem is in the lung.
Updated 2026-11-01
Also called: Alveolar–arterial gradient, PAO₂
What it is
The alveolar gas equation calculates alveolar PO₂ (PAO₂) from barometric pressure, inspired O₂ fraction and PaCO₂. Its difference from the measured PaO₂ is the A–a gradient: if normal, hypoxemia comes from breathing too little or from O₂-poor air; if widened, there is a gas-exchange defect. In Bogotá (≈ 560 mmHg) normal PAO₂ is far lower than at sea level.
Equations
- FiO2
- inspired O₂ fraction (0.21 on room air)
- PB
- barometric pressure
- PH2O
- water vapour pressure at 37 °C, 47 mmHg
- R
- respiratory quotient, ≈ 0.8
FiO₂ is 0.21 at any altitude: what falls in the mountains is barometric pressure.
- PaO2
- arterial PO₂ measured on the blood gas
Use it on room air; on high FiO₂ the normal gradient widens.
Reference values
| Parameter | Value |
|---|---|
| Water vapour pressure (37 °C) | 47 mmHg |
| Respiratory quotient (R) | ≈ 0.8 |
| A–a gradient, young adult | ≈ 5–15 mmHg |
| A–a gradient, older adult | up to ≈ 20–25 mmHg |
| Barometric pressure in Bogotá | ≈ 560 mmHg |
Approximate values for a healthy adult at rest; each laboratory sets its own ranges.
Same calculation, two cities (room air)
| Step | Sea level | Bogotá (~2600 m) |
|---|---|---|
| Barometric pressure | 760 mmHg | ≈ 560 mmHg |
| Inspired PO₂: 0.21 × (PB − 47) | ≈ 150 mmHg | ≈ 108 mmHg |
| Usual PaCO₂ | 40 mmHg | ≈ 32–35 mmHg |
| PAO₂ (subtracting PaCO₂/0.8) | ≈ 100 mmHg | ≈ 65–68 mmHg |
| Expected normal PaO₂ | ≈ 85–100 mmHg | ≈ 60–70 mmHg |
Clinical notes
- Opioid overdose: hypoxemia with high PaCO₂ and a normal A–a gradient (pure hypoventilation).
- Pulmonary embolism: hypoxemia with low PaCO₂ and a widened A–a gradient.
- A Bogotá patient with PaO₂ 62 mmHg may have normal lungs; an A–a gradient calculated with 560 mmHg settles it.
Test yourself
Think of the answer, then tap the question to see it.
In Bogotá (PB 560 mmHg), room air, PaCO₂ 32 mmHg and PaO₂ 64 mmHg. What is the A–a gradient?
PAO₂ = 0.21 × (560 − 47) − 32/0.8 ≈ 108 − 40 = 68 mmHg; gradient ≈ 4 mmHg: normal for the altitude.
Hypoxemia with a normal A–a gradient and a high PaCO₂: which mechanism?
Alveolar hypoventilation: the alveolus holds little O₂ because little fresh air enters, but exchange with the blood is normal.
Why is normal PaO₂ lower in Bogotá than in Cartagena if FiO₂ is the same?
Barometric pressure is lower, so inspired and alveolar PO₂ fall even though the air is still 21% O₂.
Why does PAO₂ rise when someone hyperventilates?
PaCO₂ falls, so less CO₂ is subtracted (PaCO₂/0.8): alveolar gas becomes more like inspired gas.
Related topics
- The causes of hypoxemia
- Oxygenation: SpO₂, PaO₂, cyanosis and oxygen therapy
- Dead space and alveolar ventilation
- High altitude and acclimatization
- Reading an arterial blood gas step by step
- Ventilation–perfusion matching and West zones
Related conditions
- Pulmonary embolism
- Acute respiratory distress syndrome (ARDS)
- Chronic obstructive pulmonary disease (COPD)
In Pharmacology
Educational physiology content; not a diagnostic or treatment guide and no substitute for a health professional's advice. Values are approximate references. No doses are given.
Sources: 22.4 Gas Exchange (OpenStax (Rice University), 2022); Arterial Blood Gas (ABG) Test: MedlinePlus Medical Test (MedlinePlus, US National Library of Medicine, 2024); 22.6 Modifications in Respiratory Functions (OpenStax (Rice University), 2022); Hall JE. Guyton and Hall Textbook of Medical Physiology, 13th ed. (ch. 40). Reference book used to check facts; its text and figures are not reproduced (Elsevier, 2016).
Spotted a mistake?We are always improving for the community. Tell us what is wrong and our team will review it.Report a mistake
Representative model, for educational purposes only.