Alveolar–arterial oxygen gradient from the alveolar gas equation: PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / 0.8
FiO₂ (fraction, e.g. 0.21 for room air)
PaO₂ (arterial)
PaCO₂ (arterial)
Barometric pressure (optional — 760 mmHg at sea level if empty)
Enter FiO₂, PaO₂ and PaCO₂ to calculate
About this score
When to use
Calculates the alveolar oxygen pressure from the alveolar gas equation and the difference to arterial PaO₂ — the A–a gradient. [1]
Pearls and pitfalls
It assumes a respiratory quotient of 0.8, water vapour pressure of 47 mmHg at 37 °C and 760 mmHg at sea level unless a barometric pressure is entered; no age-adjusted normal value is applied. [1, 2]
Summarised from the numbered sources under Evidence. Check the source before relying on a statement.
Evidence
[1] Original publication
Cruickshank S, Hirschauer N. The alveolar gas equation. Derives the alveolar oxygen partial pressure from the inspired oxygen fraction, barometric pressure, water vapour pressure and arterial PaCO₂ divided by the respiratory quotient (0.8); the A–a gradient is the difference between this alveolar value and the measured arterial PaO₂.
Continuing Education in Anaesthesia, Critical Care & Pain, 2004
[2] Note on this tool
Simplified form used here: PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / 0.8, with 47 mmHg water vapour pressure at 37 °C and 760 mmHg at sea level unless a barometric pressure is entered. No age-adjusted normal value is applied.
Last reviewed: 2026-10
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