What is a normal A-a gradient?

Approximately 2.5 + 0.21 × age mmHg on room air. For a 20-year-old it is about 7 mmHg; for a 70-year-old, about 17 mmHg. Add ~5-10 mmHg as the upper limit of normal.

Why does the A-a gradient increase with age?

Aging reduces ventilation-perfusion matching due to loss of elastic recoil, airway closure at higher lung volumes, and decreased diffusing capacity. These changes mildly widen the gradient.

When is the A-a gradient normal despite hypoxemia?

In pure hypoventilation (e.g., opiate overdose, neuromuscular weakness) and at high altitude. Both cause low PaO₂ but the gradient remains normal because gas exchange itself is intact.

What is the P/F ratio used for?

The P/F ratio (PaO₂/FiO₂) is used in the Berlin ARDS definition: mild ≤300, moderate ≤200, severe ≤100. It provides a FiO₂-normalized assessment of oxygenation.

Why do I need to know the FiO₂?

The alveolar gas equation requires FiO₂ to calculate PAO₂. On supplemental oxygen, the normal A-a gradient widens, so interpretation differs from room air values.

What is the respiratory quotient (RQ)?

RQ is the ratio of CO₂ produced to O₂ consumed. It is 0.8 for a mixed diet, 1.0 for pure carbohydrates, and 0.7 for pure fat. It affects the alveolar gas equation denominator.

A-a Gradient Calculator

Calculate the alveolar-arterial oxygen gradient from ABG values. Includes P/F ratio, expected gradient by age, altitude adjustment, and differential diagnosis table.

⚠️ Medical Disclaimer: For clinical education only. ABG interpretation requires full clinical context and should be performed by qualified healthcare providers.

PaO₂ (arterial)

mmHg

PaCO₂

mmHg

FiO₂

Age

years

Altitude

feet

Respiratory Quotient

A-a Gradient

14.7 mmHg

Normal

Expected for age 50: 13 mmHg (upper normal ≈ 23)

PAO₂ (Alveolar)

99.7 mmHg

Calculated alveolar oxygen partial pressure

A-a Gradient

14.7 mmHg

✓ Within normal range for age

Expected Gradient

13 mmHg

Formula: 2.5 + 0.21 × age (50)

P/F Ratio

405

Normal — PaO₂/FiO₂ ratio

Est. Shunt Fraction

8.9%

Approximate intrapulmonary shunt (simplified calculation)

Barometric Pressure

760 mmHg

Adjusted for altitude above sea level

Differential Diagnosis by A-a Gradient

A-a Gradient	PaO₂	Condition
Normal A-a	Low	Hypoventilation (CNS, neuromuscular, obesity)
Elevated	Low	V/Q mismatch (PE, pneumonia, COPD, asthma)
Elevated	Low	Shunt (ARDS, AVM, atelectasis, PFO)
Elevated	Low	Diffusion impairment (ILD, emphysema)
Normal A-a	Low	Low FiO₂ (high altitude)
Normal A-a	Normal/High	Normal

P/F Ratio Interpretation

P/F Ratio	Interpretation
≥ 400	Normal gas exchange
300-399	Mild impairment
200-299	Moderate impairment / Mild ARDS
100-199	Severe impairment / Moderate ARDS
< 100	Very severe / Severe ARDS

A-a Gradient Scale

▼

020406080+

Planning notes, formulas, and examples

About the A-a Gradient Calculator

The A-a Gradient Calculator computes the alveolar-arterial oxygen difference from arterial blood gas (ABG) values using the alveolar gas equation. It is a standard way to sort out hypoxemia by separating low ventilation from gas-exchange problems such as V/Q mismatch, shunt, and diffusion impairment.

The alveolar gas equation estimates alveolar oxygen pressure (PAO₂) from inspired oxygen fraction (FiO₂), barometric pressure, water vapor pressure, arterial CO₂, and the respiratory quotient. Subtracting the measured arterial PaO₂ gives the A-a gradient, which normally rises with age and with supplemental oxygen.

The calculator also reports the P/F ratio for a quick bedside oxygenation check, adjusts for altitude, and shows a simplified intrapulmonary shunt estimate. Presets cover common scenarios such as room air, COPD, pulmonary embolism, and ARDS.

When This Page Helps

The A-a gradient is most useful when the equation, age adjustment, and P/F ratio can be reviewed together instead of as separate mental steps. This page keeps those values in one place so it is easier to see whether hypoxemia looks more like low ventilation or a gas-exchange problem.

How to Use the Inputs

Enter PaO₂ from the arterial blood gas result.
Enter PaCO₂ from the same ABG.
Set the FiO₂ (21% for room air, or the supplemental oxygen percentage).
Enter patient age for age-adjusted expected gradient.
Optionally adjust altitude if testing above sea level.
RQ defaults to 0.8 (typical mixed diet); adjust if needed.
Review the A-a gradient classification and differential diagnosis table.

Formula used

PAO₂ = FiO₂ × (PAtm − PH₂O) − (PaCO₂ / RQ)
A-a Gradient = PAO₂ − PaO₂
Expected A-a Gradient = 2.5 + 0.21 × Age
P/F Ratio = PaO₂ / FiO₂
PAtm at altitude = 760 × (1 − 2.26 × 10⁻⁵ × alt_ft)^5.256

Example Calculation

Result: PAO₂ = 112.2 mmHg, A-a Gradient = 42.2 mmHg (elevated), P/F ratio = 333

At sea level with FiO₂ 21% and RQ 0.8, PAO₂ = 0.21 × (760 − 47) − (30 / 0.8) = 112.2 mmHg. Subtracting PaO₂ 70 gives an A-a gradient of 42.2 mmHg. Expected gradient for age 50 is about 13 mmHg, so this widened gradient fits a gas-exchange problem such as V/Q mismatch, shunt, or diffusion impairment.

Tips & Best Practices

Always draw ABGs at a known FiO₂ — estimating FiO₂ from nasal cannula flow is unreliable.
The A-a gradient widens on supplemental O₂; compare against age-expected values at that FiO₂.
A normal A-a gradient with elevated PaCO₂ points to hypoventilation as the cause of hypoxemia.
Very high A-a gradients (>40) on room air suggest shunt or severe V/Q mismatch.
The P/F ratio is easier to calculate bedside and is preferred for ARDS classification.
At altitude, adjust barometric pressure — the standard equation assumes 760 mmHg at sea level.

Clinical Approach to Hypoxemia Using the A-a Gradient

The first step in evaluating hypoxemia is calculating the A-a gradient. If normal, consider hypoventilation (elevated PaCO₂) or low FiO₂ (high altitude). If elevated, the differential includes V/Q mismatch (most common, responds to supplemental O₂), intrapulmonary shunt (does not respond to O₂), and diffusion impairment (reflects impaired gas transfer across the alveolar-capillary membrane).

Understanding Shunt vs. V/Q Mismatch

True shunt (blood bypassing ventilated alveoli) does not improve with supplemental oxygen because the shunted blood never contacts alveolar gas. V/Q mismatch (partially ventilated regions) does improve because increasing FiO₂ raises PAO₂ in poorly ventilated units. A "shunt study" with 100% FiO₂ can distinguish the two — persistent hypoxemia on 100% O₂ confirms shunt.

Altitude and Barometric Pressure Effects

At 5,000 feet, barometric pressure drops to ~632 mmHg, reducing PAO₂ by about 17 mmHg compared to sea level. This alone can lower PaO₂ into the 70s while maintaining a normal A-a gradient. Always adjust for altitude when interpreting ABGs obtained in mountain communities or during air transport.

Sources & Methodology

Last updated: March 27, 2026

Methodology

This page applies the alveolar gas equation to estimate alveolar oxygen pressure from the entered FiO₂, barometric pressure, water-vapor pressure, arterial carbon dioxide, and respiratory quotient, then subtracts the measured PaO₂ to report the A-a gradient. It also shows the P/F ratio, an age-expected gradient reference, and a simplified shunt estimate to help place the oxygenation problem in context.

The page is meant to support bedside interpretation of hypoxemia, not to replace full blood-gas review or ventilator assessment. The displayed shunt fraction is only a simplified estimate, and diagnosis still depends on the patient’s oxygen setting, ventilation status, and the broader respiratory picture.

Sources

Blood Gas Analysis and Hemoximetry (American Association for Respiratory Care)
Murray & Nadel's Textbook of Respiratory Medicine (Elsevier) — Standard reference for the alveolar gas equation, A-a gradient interpretation, and oxygenation physiology.

Frequently Asked Questions

Approximately 2.5 + 0.21 × age mmHg on room air. For a 20-year-old it is about 7 mmHg; for a 70-year-old, about 17 mmHg. Add ~5-10 mmHg as the upper limit of normal.