- Enter the PaO₂ and PaCO₂ (mm Hg) from the arterial blood gas, and the FiO₂ as a percentage (21 % on room air; higher on supplemental oxygen).
- The calculator computes the alveolar oxygen tension (PAO₂) and the A-a gradient (PAO₂ − PaO₂) automatically.
- Optionally enter the patient's age to compare the A-a gradient with the expected upper-normal value (Age/4 + 4 on room air).
- Optionally adjust the atmospheric pressure (default 760 mm Hg) for altitude.
- A gradient within the expected range with hypoxemia suggests hypoventilation or low inspired oxygen; an elevated gradient suggests impaired gas exchange (V/Q mismatch, shunt, diffusion impairment).
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When to Use
Use the A-a gradient when evaluating a patient with hypoxemia to localize the underlying mechanism. After obtaining an arterial blood gas, calculate the alveolar oxygen tension (PAO₂) from the FiO₂, atmospheric pressure, and PaCO₂, then subtract the measured PaO₂. A normal A-a gradient with hypoxemia points to hypoventilation or a low inspired oxygen fraction (e.g., high altitude); an elevated A-a gradient points to a problem at the alveolar–capillary interface — V/Q mismatch, right-to-left shunt, or diffusion impairment.
Appropriate population
Adults with hypoxemia or unexplained dyspnea in whom an arterial blood gas is available — pneumonia, pulmonary embolism, pulmonary edema (cardiogenic or non-cardiogenic), ARDS, interstitial lung disease, COPD, and suspected hypoventilation (opioid or sedative effect, neuromuscular weakness). In CKD and volume-overloaded patients, the A-a gradient helps distinguish pulmonary edema / cardiogenic causes (elevated gradient) from pure hypoventilation (normal gradient) as the source of dyspnea.
When NOT to rely on it
The Age/4 + 4 upper-normal rule applies to room air. On supplemental oxygen the expected gradient widens substantially and the simple age rule no longer holds, so interpretation becomes less reliable — note the FiO₂ when reading the result. The calculation also assumes a steady state and an accurate, arterial (not venous) sample, and the simplified alveolar gas equation uses a fixed respiratory quotient (R = 0.8) and water vapor pressure (47 mm Hg). Always integrate with the clinical picture, chest imaging, and the response to oxygen.
Pearls & Pitfalls
Normal widens with age
There is no single "normal" A-a gradient — it rises with age. A practical upper limit on room air is Age/4 + 4 mm Hg (an alternative is 2.5 + 0.21 × Age). A young adult may sit at 5–10 mm Hg, while a healthy 80-year-old can reach the mid-20s. Always compare the measured gradient to the age-expected value, not to a fixed cutoff.
It separates the two kinds of hypoxemia
The gradient is the single best bedside way to split hypoxemia into its two broad mechanisms. A normal gradient with a low PaO₂ means the lung is exchanging gas normally and the problem is upstream — hypoventilation (high PaCO₂) or a low inspired oxygen fraction (altitude). An elevated gradient means oxygen transfer across the alveolar–capillary membrane is impaired (V/Q mismatch, shunt, diffusion impairment).
Pitfalls
(1) The Age/4 + 4 rule is for room air; on supplemental oxygen the expected gradient widens and the rule overcalls "abnormal." (2) Use a true arterial sample — a venous gas invalidates the calculation. (3) Remember FiO₂ is entered as a percentage here (21 for room air), and the equation converts it to a fraction internally. (4) The simplified equation fixes R = 0.8 and PH₂O = 47 mm Hg; extremes of diet, temperature, or hyperventilation shift these slightly. (5) A normal gradient does not exclude lung disease if the patient is hyperventilating or on oxygen.
Why Use It
The A-a gradient turns a single number — the PaO₂ — into a statement about where hypoxemia is coming from. A patient breathing room air with a PaO₂ of 60 mm Hg could be hypoventilating from opioids (normal gradient, treat the sedation) or drowning in pulmonary edema, pneumonia, or pulmonary embolism (wide gradient, treat the lung). Without the gradient, those very different problems look identical on the oximeter. By comparing the measured gradient to the age-expected value, the calculator converts a vague impression that "the oxygen is low" into a defensible conclusion about the mechanism. In CKD and volume-overloaded patients in particular, it helps decide whether dyspnea reflects fluid in the lungs (elevated gradient) versus a non-pulmonary cause, guiding decisions about diuresis, dialysis, and respiratory support.
A-a Gradient — Alveolar–arterial Oxygen Gradient
Enter the PaO₂, PaCO₂, and FiO₂ to compute the alveolar oxygen tension (PAO₂) and the A-a gradient. Optionally add the patient's age to compare the gradient with the age-expected upper limit, and adjust the atmospheric pressure for altitude.
⚕ PAO₂ = (FiO₂ × (Patm − 47)) − PaCO₂ / 0.8, using PH₂O = 47 mm Hg and R = 0.8; A-a gradient = PAO₂ − PaO₂. The age-expected upper limit (Age/4 + 4) applies to room air; on supplemental oxygen the expected gradient widens and interpretation is less reliable. For licensed clinicians; not a substitute for individualized assessment.
Next Steps
Use the gradient — compared to the age-expected value — to localize hypoxemia and direct the next move.
- Normal A-a gradient with hypoxemia: the lung is exchanging gas normally. Look for hypoventilation (check the PaCO₂ — opioids, sedatives, neuromuscular weakness, central causes) or a low inspired oxygen (high altitude). Treat the cause of hypoventilation and reassess.
- Elevated A-a gradient: gas exchange is impaired. Consider V/Q mismatch, shunt, or diffusion impairment — pulmonary edema, pneumonia, pulmonary embolism, ARDS, or interstitial lung disease. Pursue chest imaging, assess the response to supplemental oxygen, and treat the underlying lung process.
- In CKD / volume overload: an elevated gradient supports pulmonary edema as the cause of dyspnea — escalate diuresis or dialysis and consider respiratory support; a normal gradient points away from the lungs.
- Pair this with the P/F ratio to grade oxygenation impairment and the ABG analyzer for the full acid–base and oxygenation picture.
Evidence & References
Formula
| Quantity | Formula |
|---|---|
| Alveolar PAO₂ (mm Hg) | (FiO₂ × (Patm − 47)) − PaCO₂ / 0.8 |
| A-a gradient (mm Hg) | PAO₂ − PaO₂ |
| Expected upper limit (room air) | Age / 4 + 4 (alt: 2.5 + 0.21 × Age) |
| Constants | PH₂O = 47 mm Hg · R = 0.8 · Patm = 760 mm Hg (sea level) |
Interpretation
| Finding | Interpretation |
|---|---|
| A-a within age-expected limit | Normal gas exchange; hypoxemia (if present) from hypoventilation or low inspired O₂ |
| A-a mildly elevated | Early or modest impairment of gas exchange (V/Q mismatch) |
| A-a markedly elevated | Significant impaired gas exchange — shunt, severe V/Q mismatch, or diffusion impairment (edema, pneumonia, PE, ARDS, ILD) |
The simplified alveolar gas equation assumes a fixed respiratory quotient (R = 0.8) and water vapor pressure (47 mm Hg). The age-expected upper limit is valid on room air; supplemental oxygen widens the normal gradient and reduces the reliability of the age rule.
References
- West JB. Respiratory Physiology: The Essentials. 10th ed. Wolters Kluwer; 2016.
- Helmholz HF Jr. The abbreviated alveolar air equation. Chest. 1979;75(6):748.
- Story DA. Alveolar oxygen partial pressure, alveolar-arterial oxygen difference, and physiologic dead space calculation. Anesthesiology. 1996;84(4):1011.
