A–a Gradient Calculator (Alveolar Gas Equation)

Enter FiO₂, PaCO₂ and PaO₂ from an arterial blood gas to calculate alveolar PO₂ with the alveolar gas equation and the alveolar–arterial (A–a) oxygen gradient. Add age to compare with the expected normal.

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Written and reviewed by the Kinase Medical Team · Last reviewed 30 September 2026

Quick Answer

PAO₂ = FiO₂ × (760 − 47) − PaCO₂ ÷ 0.8 at sea level, and A–a gradient = PAO₂ − PaO₂. On room air the expected upper limit is about age ÷ 4 + 4 mmHg. A normal gradient with hypoxaemia points to hypoventilation or low inspired oxygen; a raised gradient points to V/Q mismatch, shunt or a diffusion problem.

For learning — not for clinical decisions. This calculator is a study aid for exam preparation. Check every result against your institution's protocols and senior advice before acting on it.

A–a gradient calculator

Room air = 21%

Constants (sea level, 37 °C)

760 at sea level

47 at 37 °C

0.8 usual

Enter FiO₂, PaCO₂ and PaO₂ from the same blood gas.

How it's calculated

Alveolar gas equation (simplified)
PAO₂ = FiO₂ × (Patm − PH₂O) − PaCO₂ ÷ RQ
Patm 760 mmHg (sea level), PH₂O 47 mmHg (37 °C), RQ 0.8. Change Patm for altitude.
A–a gradient
A–a = PAO₂ − PaO₂
Expected A–a on room air
≈ age ÷ 4 + 4 (alternative: (age + 10) ÷ 4)
Two StatPearls chapters give these two estimates; both rise about 1 mmHg for every 4 years of age.

How to interpret the result

Hypoxaemia patterns from StatPearls (Hypoxia and Hypoxemia, NBK482316).
PatternPaCO₂A–a gradientNote
HypoventilationHighNormalAlveolar and arterial PO₂ fall together
Low inspired O₂ (e.g. altitude)NormalNormalLungs transfer oxygen normally
V/Q mismatch (e.g. pneumonia, COPD)NormalRaisedCorrects with 100% O₂
Right-to-left shunt (e.g. dense consolidation, intracardiac shunt)NormalRaisedDoes not correct with 100% O₂
Diffusion impairment (e.g. interstitial lung disease)NormalRaisedAlveolar–capillary membrane problem

Worked example

A 40-year-old on room air: PaCO₂ 40 mmHg, PaO₂ 90 mmHg.

PAO₂ = 0.21 × (760 − 47) − 40 ÷ 0.8 = 149.7 − 50 = 99.7 mmHg. A–a gradient = 99.7 − 90 = 9.7 mmHg. Expected for age ≈ 40 ÷ 4 + 4 = 14 mmHg → normal.

Same patient with PaCO₂ 30 and PaO₂ 60: PAO₂ = 149.7 − 37.5 = 112.2; gradient = 52.2 mmHg → raised, so the hypoxaemia is due to a lung (alveolar–capillary) problem.

An opioid overdose with PaCO₂ 80 and PaO₂ 45: PAO₂ = 149.7 − 100 = 49.7; gradient = 4.7 mmHg → normal, so hypoventilation alone explains the hypoxaemia.

Limitations and common pitfalls

  • Age-based normal values are for room air. On supplemental oxygen the gradient widens even in healthy lungs, so compare trends, not a fixed cut-off.
  • The simplified equation assumes a steady state and sea-level pressure. At altitude, enter the local barometric pressure.
  • Use PaCO₂ and PaO₂ from the same arterial sample, taken at a known FiO₂.
  • A negative gradient is not physiological — recheck the values and the FiO₂.

Sources

  1. StatPearls — Alveolar Gas Equation (NCBI Bookshelf, NBK482268)
  2. StatPearls — Physiology, Alveolar to Arterial Oxygen Gradient (NCBI Bookshelf, NBK545153)
  3. StatPearls — Hypoxia and Hypoxemia (NCBI Bookshelf, NBK482316)
  4. StatPearls — Oxygenation Status and Pulse Oximeter Analysis (NCBI Bookshelf, NBK592401)

For learning — not for clinical decisions. Reference ranges and cut-offs vary between laboratories and guidelines.

Frequently Asked Questions

What is the alveolar gas equation?▼
PAO₂ = FiO₂ × (Patm − PH₂O) − PaCO₂ ÷ RQ. At sea level Patm is 760 mmHg, water vapour pressure at body temperature is 47 mmHg and the respiratory quotient is taken as 0.8. On room air with a PaCO₂ of 40 this gives a PAO₂ of about 100 mmHg.
What is a normal A–a gradient?▼
It rises with age. A common estimate of the upper normal limit on room air is age ÷ 4 + 4 mmHg; another StatPearls chapter uses (age + 10) ÷ 4. Quoted normal values span roughly 5–25 mmHg depending on age.
Which causes of hypoxaemia have a normal A–a gradient?▼
Hypoventilation (high PaCO₂) and low inspired oxygen, for example at high altitude. In both, alveolar oxygen is low, so arterial oxygen is low too, but the lungs transfer oxygen normally.
Which causes of hypoxaemia raise the A–a gradient?▼
Problems at the alveolar–capillary unit: V/Q mismatch, right-to-left shunt and diffusion impairment — for example pneumonia, pulmonary oedema or interstitial lung disease. Hypoxaemia from V/Q mismatch improves with 100% oxygen; a true shunt does not.
Does supplemental oxygen change the A–a gradient?▼
Yes. When FiO₂ is above room air, alveolar PO₂ rises faster than arterial PO₂, so the gradient widens even in healthy lungs. The age-based normal values apply only to room air.
Why use RQ 0.8 in the equation?▼
The respiratory quotient is the ratio of CO₂ produced to O₂ consumed. The steady-state value of 0.8 is the standard assumption, so PaCO₂ ÷ 0.8 estimates how much alveolar oxygen is displaced by CO₂.
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