Alveolar Gas Equation Calculator

Calculate alveolar pO2, A-a gradient, and hypoxemia cause using the alveolar gas equation.

Fraction inspired O2 FiO2

0.21=room air, 1.0=100%

Barometric pressure Pb (mmHg) (mmHg)

Sea level=760, Denver=640

Arterial pCO2 (mmHg) (mmHg)

Respiratory quotient R

Usually 0.8

Measured arterial pO2 (mmHg) (mmHg)

Please check your inputs and try again.

Why 47 mmHg Is Subtracted First

Inspired air is fully saturated with water vapour by the time it reaches the alveoli. At body temperature that vapour exerts 47 mmHg regardless of barometric pressure, and it occupies space unavailable to other gases.

PAO₂ = FiO₂(P_b − 47) − PaCO₂/R

Because the 47 mmHg is constant while barometric pressure falls with altitude, water vapour occupies a progressively larger fraction of what is available. This is one reason altitude hypoxia worsens faster than barometric pressure alone suggests.

Location	P_b	PAO₂ on room air
Sea level	760	100 mmHg
Denver	640	74 mmHg
La Paz	495	44 mmHg
Everest summit	253	~30 mmHg*

What the A–a Gradient Distinguishes

The gradient separates two entirely different causes of hypoxia, which require opposite treatments.

A–a gradient	Cause	Responds to supplemental O₂?
Normal	Hypoventilation or low FiO₂	Yes — but treat the ventilation
Raised	V/Q mismatch	Yes
Raised	Shunt	Poorly — blood bypasses ventilated lung
Raised	Diffusion impairment	Yes

The shunt case is the clinically decisive one. In V/Q mismatch, raising FiO₂ improves oxygenation because poorly ventilated alveoli still receive some gas. In a true shunt, blood bypasses ventilated alveoli entirely — so oxygen barely helps, which is itself diagnostic.

Normal gradient rises with age, approximated by (age/4) + 4. A gradient of 20 is normal at 70 and clearly abnormal at 20.

The Respiratory Quotient Term

Dividing PaCO₂ by R accounts for the fact that slightly more oxygen is consumed than carbon dioxide produced on a mixed diet, so alveolar volume falls marginally. R is conventionally 0.8, though it approaches 1.0 on a pure carbohydrate diet and 0.7 on pure fat.

Worked Examples

Example 1: Room air: FiO2=0.21, Pb=760, pCO2=40

PAO2=(760-47)×0.21-40/0.8

Result: PAO2=99.7mmHg, A-a=99.7-95=4.7mmHg

Normal A-a gradient

Example 2: High altitude (Denver): Pb=640

PAO2=(640-47)×0.21-40/0.8

Result: PAO2=74.5mmHg — significant reduction

Explains altitude hypoxia even with normal lungs

Example 3: Distinguishing shunt from V/Q mismatch

Hypoxia unresponsive to high FiO₂

Result: Shunt

Blood bypasses ventilated lung, so added oxygen never reaches it. V/Q mismatch would improve, since poorly ventilated units still receive some gas.

Example 4: Why altitude is worse than pressure suggests

Everest summit, P_b = 253 mmHg, pCO₂ reduced to 10 by hyperventilation

Result: PAO₂ around 30 mmHg

The constant 47 mmHg of water vapour consumes nearly a fifth of total pressure. At a normal pCO₂ of 40 the equation returns a negative value — survival depends on extreme hyperventilation dropping pCO₂ to around 10 mmHg.

Common Mistakes

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Forgetting to subtract water vapour

Saturated inspired air exerts 47 mmHg at body temperature. Omitting it overestimates alveolar oxygen substantially, especially at altitude.

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Using a fixed normal A–a gradient

It rises with age, roughly (age/4) + 4. A gradient of 20 is normal at 70 and abnormal at 20.

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Expecting oxygen to correct a shunt

Shunted blood bypasses ventilated alveoli entirely, so raising FiO₂ helps little. Poor response to oxygen is itself diagnostic.

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Assuming water vapour pressure changes with altitude

It depends only on body temperature and stays at 47 mmHg. Because barometric pressure falls, it occupies a growing fraction of the total.

Frequently Asked Questions

Why subtract water vapor pressure?

At 37°C, saturated water vapor pressure = 47 mmHg. Airways fully humidify inspired air, reducing partial pressure of O2 and N2. Always subtract 47 from Pb before calculating PAO2.

FiO2 supplemental O2?

Nasal cannula 2L/min: FiO2≈0.28. Simple mask 6L/min: FiO2≈0.4. Non-rebreather 15L/min: FiO2≈0.85. Intubated with 100%: FiO2=1.0. Higher FiO2 raises PAO2 proportionally, useful to distinguish hypoventilation (A-a normal) from V/Q mismatch (A-a elevated).

Why subtract 47 mmHg?

Because inspired air becomes fully saturated with water vapour at body temperature, and that vapour occupies pressure unavailable to other gases.

What is a normal A–a gradient?

Roughly (age/4) + 4 mmHg. It widens with age as ventilation-perfusion matching deteriorates.

How does the gradient distinguish causes of hypoxia?

A normal gradient indicates hypoventilation or low inspired oxygen. A raised gradient indicates V/Q mismatch, shunt or diffusion impairment.

Why doesn't oxygen correct a shunt?

Because shunted blood never contacts ventilated alveoli. Raising inspired oxygen cannot reach it, which is why poor response suggests shunt.