Alveolar Gas Equation Calculator
Calculate alveolar oxygen pressure (PAO₂) from FiO₂, atmospheric pressure, water vapor pressure, PaCO₂, and respiratory quotient.
Shows A-a gradient context.
The alveolar gas equation calculates the partial pressure of oxygen in the alveoli (PAO₂), the maximum oxygen pressure available for diffusion into pulmonary capillary blood. Comparing PAO₂ to the measured arterial PaO₂ gives the A-a gradient, one of the most useful bedside numbers in pulmonary medicine.
The formula: PAO₂ = FiO₂ × (P_atm − P_H₂O) − (PaCO₂ ÷ RQ)
The equation accounts for two facts about inhaled gas: it is humidified inside the airway (water vapor displaces some of the oxygen), and oxygen is consumed as carbon dioxide is produced (the respiratory quotient links the two).
Standard input values at sea level, room air:
| Variable | Typical value | Notes |
|---|---|---|
| FiO₂ | 0.21 | Room air. Supplemental oxygen raises this (nasal cannula at 4 L/min ≈ 0.36). |
| P_atm | 760 mmHg | Sea level. Drops about 10 mmHg per 100 m of altitude. |
| P_H₂O | 47 mmHg | Body temperature (37 °C). Effectively constant in patients. |
| PaCO₂ | 40 mmHg | Normal arterial CO₂. Hyperventilation lowers it, hypoventilation raises it. |
| RQ | 0.8 | Mixed diet. Pure carbohydrate diet → 1.0. Pure fat diet → 0.7. |
Worked example: healthy adult at sea level
FiO₂ = 0.21, P_atm = 760, P_H₂O = 47, PaCO₂ = 40, RQ = 0.8 PAO₂ = 0.21 × (760 − 47) − (40 ÷ 0.8) PAO₂ = 0.21 × 713 − 50 = 149.7 − 50 = 99.7 mmHg
Expected arterial PaO₂ in this patient is about 95 mmHg, giving an A-a gradient of roughly 5 mmHg, well within the normal 5 to 15 range for young adults.
Worked example: mountaineer at altitude
A climber at 5,500 m has P_atm ≈ 380 mmHg and may hyperventilate to PaCO₂ = 25 mmHg. PAO₂ = 0.21 × (380 − 47) − (25 ÷ 0.8) = 69.9 − 31.25 = 38.7 mmHg
Significantly reduced. This is why supplemental oxygen is standard above 5,000 m, and why high-altitude pulmonary edema can develop quickly when even modest illness limits ventilation.
The A-a gradient: why this calc matters
A-a gradient = PAO₂ (calculated) − PaO₂ (measured from arterial blood gas)
Normal A-a gradient on room air:
- Healthy young adult: 5 to 15 mmHg
- Older adult: rises with age, approximately (age ÷ 4) + 4
An elevated A-a gradient with hypoxemia suggests one of four mechanisms: V/Q mismatch (most common, includes pneumonia and PE), shunt (cardiac or atelectasis), diffusion impairment (interstitial lung disease), or low mixed venous O₂. A normal A-a gradient with hypoxemia points to hypoventilation or low inspired oxygen as the cause.
Common pitfalls
- Forgetting that FiO₂ on room air is 0.21, not 21
- Using P_atm = 760 for patients at altitude (Denver, Mexico City, La Paz all see meaningfully lower values)
- Not adjusting expected normal A-a gradient for age in older patients
- Using arterial PCO₂ when only end-tidal CO₂ is available; the two diverge in disease states
When to use the alveolar gas equation
- Calculating the A-a gradient to evaluate the cause of hypoxemia
- Assessing oxygenation at high altitudes for travel medicine and aerospace medicine
- Adjusting supplemental oxygen levels in hospitalized patients
- Teaching pulmonary physiology, since it ties together ventilation, diffusion, and gas physics in a single elegant equation
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