# Alveolar–arterial gradient

The alveolar–arterial gradient (A-a gradient, or P(A–a)O₂) is the difference between the partial pressure of oxygen in the alveoli (P\(_{A}\)O₂) and the partial pressure of oxygen in arterial blood (P\(_{a}\)O₂), measured in mmHg. It is used to diagnose the cause of hypoxemia, because a normal gradient points to causes outside the alveolar–capillary unit while a widened gradient points to lung pathology.<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup><sup> • </sup><sup>[2](https://www.ncbi.nlm.nih.gov/books/NBK545153/?report=printable)</sup>

| Key fact | Detail |
|---|---|
| Definition | A-a gradient = P\(_{A}\)O₂ − P\(_{a}\)O₂; the alveolar value is calculated, the arterial value is measured on an arterial blood gas<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> |
| Alveolar gas equation | P\(_{A}\)O₂ = (P\(_{B}\) − P\(_{H2O}\)) × F\(_{I}\)O₂ − P\(_{a}\)CO₂/R, with barometric pressure 760 mmHg at sea level, water vapor pressure 47 mmHg, and respiratory quotient R = 0.8<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> |
| Normal values | 5–15 mmHg overall; 5–10 mmHg in a normal young adult, with P\(_{A}\)O₂ about 105 mmHg and P\(_{a}\)O₂ about 100 mmHg<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> |
| Age adjustment | Normal A-a gradient = (age in years + 10) / 4; an alternative rule is that it should be ≤ 0.3 × age<sup>[3](https://www.ncbi.nlm.nih.gov/books/NBK482268/)</sup><sup> • </sup><sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> |
| Effect of oxygen therapy | The gradient typically increases by 5 to 7 mmHg for every 10% increase in F\(_{I}\)O₂<sup>[3](https://www.ncbi.nlm.nih.gov/books/NBK482268/)</sup> |
| Normal gradient in hypoxemia | Decreased inspired P\(_{O2}\) (altitude) or hypoventilation<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup><sup> • </sup><sup>[11](https://www.ncbi.nlm.nih.gov/books/NBK371/?report=reader)</sup> |
| Widened gradient in hypoxemia | Ventilation/perfusion mismatch, shunt, or diffusion limitation<sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10910131/)</sup> |

## Calculation

The arterial P\(_{O2}\) is measured directly on an arterial blood gas sample. The alveolar P\(_{O2}\) cannot be sampled simply, so it is calculated from the alveolar gas equation:<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup>

\[ P_{A}O_{2} = (P_{B} - P_{H_{2}O}) \times F_{I}O_{2} - \frac{P_{a}CO_{2}}{R} \]

Here P\(_{B}\) is barometric pressure (760 mmHg at sea level), P\(_{H2O}\) is the water vapor pressure of fully saturated inspired gas (47 mmHg at body temperature), F\(_{I}\)O₂ is the fraction of inspired oxygen, P\(_{a}\)CO₂ is the arterial carbon dioxide tension (normal range 35–45 mmHg), and R is the gas exchange ratio, also called the respiratory quotient, usually taken as 0.8.<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> A simplified form of the equation is P\(_{A}\)O₂ = F\(_{I}\)O₂ × 713 − P\(_{a}\)CO₂/0.8.<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup>

**Worked example.** For a normal person breathing room air (F\(_{I}\)O₂ = 0.21) at sea level with a P\(_{a}\)CO₂ of 40 mmHg:<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup>

\[ P_{A}O_{2} = (760 - 47) \times 0.21 - \frac{40}{0.8} = 99.73 \text{ mmHg} \]

Subtracting a typical arterial P\(_{O2}\) of about 100 mmHg gives the small normal gradient. Carbon dioxide is a crucial variable: a significant rise in CO₂ displaces oxygen within the alveoli and lowers the calculated P\(_{A}\)O₂, which is one route to hypoxemia.<sup>[3](https://www.ncbi.nlm.nih.gov/books/NBK482268/)</sup>

## Normal values and age

The gradient exists even in health because of small ventilation–perfusion inequalities, shunt, and diffusion disequilibrium, so a physiologic A-a gradient is expected and it changes with age.<sup>[2](https://www.ncbi.nlm.nih.gov/books/NBK545153/?report=printable)</sup> A commonly used bedside estimate of the upper limit of normal is (age in years + 10) / 4.<sup>[3](https://www.ncbi.nlm.nih.gov/books/NBK482268/)</sup> The Westmead Anaesthetic Manual states the gradient increases with age and should be ≤ 0.3 × age.<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> [Reference](https://www.edgepedia.org/reference) values from a general medical text place the upper limit of normal at about 3 kPa (23 mmHg) at age 40, rising to 5 kPa (38 mmHg) at age 80 when breathing room air.<sup>[5](https://www.sciencedirect.com/topics/nursing-and-health-professions/arterial-oxygen-saturation)</sup>

[Oxygen therapy](https://www.edgepedia.org/oxygen-therapy) changes the number itself. The gradient typically increases by 5 to 7 mmHg for every 10% increase in F\(_{I}\)O₂, so an expected value must be interpreted against the oxygen the patient is receiving.<sup>[3](https://www.ncbi.nlm.nih.gov/books/NBK482268/)</sup>

## Interpreting the gradient in hypoxemia

**Normal gradient.** If a hypoxemic patient has a normal A-a gradient, the problem is extrinsic to the lungs: the alveoli and the arterial blood fall together, so the gap between them stays within normal limits. The recognized causes are decreased partial pressure of inspired oxygen, as at altitude; hypoventilation; and hemoglobin defects or anemia.<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup><sup> • </sup><sup>[2](https://www.ncbi.nlm.nih.gov/books/NBK545153/?report=printable)</sup>

**Widened gradient.** A gradient wider than expected for the patient's age and F\(_{I}\)O₂ narrows the cause of hypoxemia to ventilation/perfusion (V/Q) mismatch, shunt, or diffusion limitation, all disorders of the alveolar–capillary unit.<sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10910131/)</sup><sup> • </sup><sup>[2](https://www.ncbi.nlm.nih.gov/books/NBK545153/?report=printable)</sup> As a general rule, any pathology of the alveolar–capillary unit raises the gradient: the alveolus may be well oxygenated while diffusion across it is poor, leaving arterial blood with lower oxygen.<sup>[6](https://www.ncbi.nlm.nih.gov/books/NBK545153/)</sup> Examples include pulmonary fibrosis and interstitial lung disease.<sup>[1](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)</sup> In acute pulmonary embolism, hypoxemia with an increased alveolar–arterial oxygen tension gradient is among the most common gas exchange abnormalities, arising from low V/Q units where ventilation to the capillaries is reduced relative to blood flow.<sup>[7](https://www.ahajournals.org/doi/pdf/10.1161/01.cir.0000097829.89204.0c?download=true)</sup>

**Response to oxygen.** The gradient also helps predict the response to supplemental oxygen. Hypoxemia from V/Q mismatch improves with added oxygen, whereas when the shunt fraction rises above 50%, P\(_{a}\)O₂ becomes essentially independent of F\(_{I}\)O₂ because capillary blood never contacts ventilated lung.<sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10910131/)</sup>

## Use in pulmonary embolism

Because arterial blood gases and the A-a gradient are sensitive indicators of pulmonary pathology, a 1993 study at Cleveland MetroHealth Medical Center examined whether a normal A-a gradient could rule out pulmonary embolism in patients undergoing ventilation/perfusion scanning for suspected PE, using records from 1988 and 1989.<sup>[8](https://pubmed.ncbi.nlm.nih.gov/8304364/)</sup> The gradient has also been incorporated into severity scores: it forms part of the Acute Physiology, Age and Chronic Health Evaluation (APACHE 2) score, although several drawbacks reduce its clinical usefulness.<sup>[9](https://ndl.ethernet.edu.et/bitstream/123456789/55613/1/3973.pdf)</sup>

## Non-invasive alternatives

The traditional measurement requires an arterial blood sample, which is invasive, time consuming, and uncomfortable, and the A-a gradient is not routinely calculated in day-to-day practice.<sup>[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC8567009/)</sup> A newer non-invasive surrogate, the oxygen deficit, measures end-tidal (alveolar) P\(_{O2}\) directly from expired gas and estimates arterial P\(_{O2}\) from pulse oximetry using the Hill equation, inverting the roles of the two measurements. It correlates well with the A-a gradient (r² ≈ 0.72 in patients with lung disease) and detects the age-related decline in gas exchange efficiency, with values of about 2 mmHg in young adults and about 8 mmHg in older subjects.<sup>[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC8567009/)</sup> The approach is reliable only at oxygen saturations of about 94% and below, where the flat upper portion of the oxygen–hemoglobin dissociation curve does not magnify small saturation errors into large P\(_{O2}\) errors.<sup>[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC8567009/)</sup>

## References

1. [A-A Gradient, Westmead Anaesthetic Manual, 5th Edition, McGraw Hill](https://accessworldmed.mhmedical.com/content.aspx?bookid=3455&sectionid=285661143)
2. [Physiology, Alveolar to Arterial Oxygen Gradient, StatPearls, NCBI Bookshelf](https://www.ncbi.nlm.nih.gov/books/NBK545153/?report=printable)
3. [Alveolar Gas Equation, StatPearls, NCBI Bookshelf](https://www.ncbi.nlm.nih.gov/books/NBK482268/)
4. [Diagnosis and Management of Acute Respiratory Failure, PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC10910131/)
5. [Arterial Oxygen Saturation, ScienceDirect Topics](https://www.sciencedirect.com/topics/nursing-and-health-professions/arterial-oxygen-saturation)
6. [Physiology, Alveolar to Arterial Oxygen Gradient, StatPearls, NCBI Bookshelf](https://www.ncbi.nlm.nih.gov/books/NBK545153/)
7. [Acute Pulmonary Embolism: Part I, Circulation](https://www.ahajournals.org/doi/pdf/10.1161/01.cir.0000097829.89204.0c?download=true)
8. [Use of the alveolar-arterial oxygen gradient in the diagnosis of pulmonary embolism, PubMed](https://pubmed.ncbi.nlm.nih.gov/8304364/)
9. [Textbook chapter on pulmonary oxygen transfer (A-a gradient and APACHE 2)](https://ndl.ethernet.edu.et/bitstream/123456789/55613/1/3973.pdf)
10. [Non-invasive Measurement of Pulmonary Gas Exchange Efficiency: The Oxygen Deficit, Frontiers in Physiology (Prisk & West, 2021)](https://pmc.ncbi.nlm.nih.gov/articles/PMC8567009/)
11. [ncbi.nlm.nih.gov](https://www.ncbi.nlm.nih.gov/books/NBK371/?report=reader)

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*Topic: Encyclopedia › Life and health › Human health and medicine › Human structure and function › Cardiovascular and lymphatic systems › Blood vessels › Pulmonary circulation*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 21, 2026 · Edited: Sep 30, 2026; Oct 21, 2026 · Last review: Oct 21, 2026*

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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license