Alveolar gas equation

6 min read Last updated April 8, 2026

Core equations (must know)

  • Full alveolar gas equation (ideal alveolar PO2): PAO2 = PIO2 − (PaCO2 / R) + F
    • PAO2: alveolar oxygen partial pressure (kPa or mmHg).
    • PIO2: inspired oxygen partial pressure = FiO2 × (PB − PH2O).
    • PaCO2 approximates PACO2 in steady state (high diffusibility of CO2).
    • R: respiratory quotient (CO2 production / O2 consumption), typically 0.8 (mixed diet).
    • F: small correction factor (usually ignored at sea level; becomes more relevant at high FiO2).
  • Common FRCA simplification at sea level: PAO2 ≈ FiO2 × (PB − PH2O) − (PaCO2 / R)
  • A–a gradient: (A–a)O2 = PAO2 − PaO2
    • Used to separate hypoxaemia due to hypoventilation/low PIO2 from V/Q mismatch/shunt/diffusion limitation.

Typical values (UK units)

  • At sea level: PB ≈ 101 kPa; PH2O at 37°C ≈ 6.3 kPa.
  • Room air: FiO2 0.21 → PIO2 ≈ 0.21 × (101 − 6.3) ≈ 19.9 kPa.
  • If PaCO2 5.3 kPa and R 0.8: PaCO2/R ≈ 6.6 kPa → PAO2 ≈ 13.3 kPa.
  • Normal A–a gradient on air: roughly 1–2 kPa in young adults; increases with age.
    • Rule of thumb (mmHg): expected A–a ≈ (Age/4) + 4; convert cautiously if using kPa.

How to use it clinically (pattern recognition)

  • Low PaO2 with normal A–a gradient: think low PIO2 (altitude) or hypoventilation (raised PaCO2).
  • Low PaO2 with raised A–a gradient: think V/Q mismatch, shunt, diffusion limitation.
    • V/Q mismatch: improves with increased FiO2.
    • Shunt (true R→L): limited response to increased FiO2.
  • On high FiO2, A–a gradient often increases even in health (because PAO2 rises markedly while PaO2 is limited by V/Q inequality and shunt).

Derivation essentials (what you may be asked to explain)

  • Concept: alveolar O2 is determined by inspired O2 delivery to alveoli minus O2 removed by blood, which is linked to CO2 added to alveoli.
  • Assumption: PACO2 ≈ PaCO2 (equilibration across alveolar-capillary membrane).
  • Link O2 uptake to CO2 output via respiratory quotient: R = VCO2/VO2 → VO2 = VCO2/R.
  • Therefore alveolar O2 falls in proportion to PaCO2/R for a given inspired O2.

Units and conversions (avoid losing marks)

  • Use consistent units throughout (kPa or mmHg).
  • Sea level constants: PB 760 mmHg ≈ 101 kPa; PH2O 47 mmHg ≈ 6.3 kPa.
  • If using mmHg: PIO2 on air ≈ 0.21 × (760 − 47) ≈ 150 mmHg.

Worked examples (typical FRCA calculations)

  • Example 1 (air, sea level): FiO2 0.21, PaCO2 5.3 kPa, R 0.8. PIO2 ≈ 19.9 kPa. PAO2 ≈ 19.9 − (5.3/0.8)= 19.9 − 6.6 = 13.3 kPa.
    • If measured PaO2 = 10.5 kPa → A–a ≈ 2.8 kPa (mildly raised depending on age).
  • Example 2 (hypoventilation): same but PaCO2 8.0 kPa. PAO2 ≈ 19.9 − (8/0.8)= 19.9 − 10 = 9.9 kPa. If PaO2 ~9 kPa → A–a ~1 kPa (normal): hypoventilation.
  • Example 3 (high FiO2): FiO2 0.6, PB 101 kPa, PH2O 6.3 → PIO2 ≈ 0.6×94.7=56.8 kPa. If PaCO2 5.3 and R 0.8: PAO2 ≈ 56.8 − 6.6 = 50.2 kPa. If PaO2 is 20 kPa → A–a ≈ 30 kPa (very raised): significant V/Q mismatch/shunt.

Clinical interpretation framework (hypoxaemia)

  • Step 1: calculate/estimate PAO2 from FiO2, PB, PH2O, PaCO2 and R.
  • Step 2: compute A–a gradient and compare with expected for age and FiO2.
  • Step 3: decide mechanism: low PIO2 vs hypoventilation vs V/Q mismatch vs shunt vs diffusion limitation.
  • Step 4: test response to oxygen (clinical): V/Q mismatch improves; shunt improves little.
State the alveolar gas equation and define each term.

Give the full equation, then the common simplification and definitions.

  • PAO2 = PIO2 − (PaCO2 / R) + F.
  • PIO2 = FiO2 × (PB − PH2O).
  • PaCO2 approximates PACO2 in steady state; R ≈ 0.8; F usually ignored at sea level.
Calculate PAO2 on room air at sea level for PaCO2 5.3 kPa and R 0.8. What is the expected order of magnitude?

Use PB 101 kPa and PH2O 6.3 kPa.

  • PIO2 ≈ 0.21 × (101 − 6.3) ≈ 19.9 kPa.
  • PaCO2/R ≈ 5.3/0.8 ≈ 6.6 kPa.
  • PAO2 ≈ 19.9 − 6.6 ≈ 13.3 kPa (i.e. ~13 kPa).
A patient on air has PaO2 7.5 kPa and PaCO2 8.5 kPa. Use the alveolar gas equation to determine whether the A–a gradient is raised and suggest the likely mechanism of hypoxaemia.

Assume sea level, R 0.8, PH2O 6.3 kPa.

  • PIO2 ≈ 19.9 kPa.
  • PAO2 ≈ 19.9 − (8.5/0.8) ≈ 19.9 − 10.6 ≈ 9.3 kPa.
  • A–a ≈ 9.3 − 7.5 = 1.8 kPa (may be normal/mildly raised depending on age).
  • Primary issue is hypoventilation (raised PaCO2 causing low PAO2).
Explain why PaCO2 is used in the alveolar gas equation rather than PACO2.

This tests assumptions and limitations.

  • In steady state, CO2 equilibrates rapidly across the alveolar-capillary membrane, so end-capillary and arterial PCO2 approximate alveolar PCO2.
  • Thus PaCO2 is a practical surrogate for PACO2; errors occur with severe V/Q mismatch, dead space, or non-steady-state conditions.
Define respiratory quotient (R). What factors change it and how does that affect PAO2?

R links CO2 production to O2 consumption.

  • R = VCO2 / VO2; typical mixed diet ≈ 0.8.
  • Carbohydrate metabolism increases R (~1.0); fat metabolism lowers R (~0.7).
  • For a given PaCO2, higher R reduces (PaCO2/R) and increases PAO2; lower R does the opposite.
What is the A–a gradient and how does it help differentiate causes of hypoxaemia?

Expect a structured answer with mechanisms.

  • (A–a)O2 = PAO2 − PaO2.
  • Normal A–a: suggests hypoventilation or low inspired O2 (altitude).
  • Raised A–a: suggests V/Q mismatch, shunt, or diffusion limitation.
A previous FRCA-style scenario: A patient on 60% oxygen has PaO2 12 kPa and PaCO2 5 kPa. Estimate PAO2 and comment on the likely pathology.

Use PB 101 kPa, PH2O 6.3 kPa, R 0.8.

  • PIO2 ≈ 0.6 × (101 − 6.3) ≈ 56.8 kPa.
  • PAO2 ≈ 56.8 − (5/0.8) ≈ 56.8 − 6.25 ≈ 50.6 kPa.
  • A–a ≈ 50.6 − 12 = 38.6 kPa: very large, consistent with major V/Q mismatch and/or shunt (e.g. atelectasis, pneumonia, ARDS).
Why does the A–a gradient often increase when FiO2 is increased, even if the lungs are unchanged?

This is a common viva point about interpreting A–a on oxygen.

  • Raising FiO2 markedly increases PAO2.
  • PaO2 does not rise proportionally due to physiological shunt and V/Q inequality (and any existing pathology), so the difference (A–a) widens.
How does altitude affect PAO2 and the A–a gradient?

Focus on PB and PIO2.

  • Altitude reduces barometric pressure (PB), reducing PIO2 = FiO2 × (PB − PH2O), so PAO2 falls.
  • In pure altitude hypoxaemia with normal lungs, A–a gradient remains normal (both PAO2 and PaO2 fall).
What are the key assumptions/limitations of the alveolar gas equation in clinical practice?

List assumptions and when they break down.

  • Steady state and accurate PaCO2 measurement; assumes PaCO2 ≈ PACO2.
  • Assumed R (often 0.8) may be wrong in unusual metabolic states or during over/underfeeding in ICU.
  • Does not directly quantify shunt fraction; A–a gradient is influenced by FiO2 and age.
In a viva, you are asked: 'How would you use the alveolar gas equation to assess whether hypoxaemia is due to hypoventilation?' Give a structured approach.

A stepwise method scores well.

  • Calculate PIO2 from FiO2 and PB/PH2O.
  • Calculate PAO2 using PaCO2 and assumed R.
  • Compute A–a = PAO2 − PaO2: if normal/near-normal, hypoventilation (or low PIO2) is likely; if raised, consider V/Q mismatch/shunt/diffusion.

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