About the A-a Gradient Calculator
The alveolar–arterial (A–a) oxygen gradient is the difference between the oxygen partial pressure in the alveoli (PAO₂, calculated with the alveolar gas equation) and the oxygen partial pressure measured in arterial blood (PaO₂). It tells you whether low blood oxygen is explained by low inspired oxygen or hypoventilation alone (normal gradient) or by a problem with gas transfer in the lungs — ventilation/perfusion mismatch, shunt or a diffusion defect (raised gradient).
Enter the inspired oxygen fraction and the PaO₂ and PaCO₂ from an arterial blood gas, plus the patient’s age. The calculator assumes body temperature (water vapour pressure 47 mmHg) and a respiratory quotient of 0.8 by default; you can change barometric pressure for altitude and the respiratory quotient if needed. It also reports the PaO₂/FiO₂ ratio and the arterial/alveolar (a/A) ratio.
The expected gradient rises with age. The common bedside estimate is age ÷ 4 + 4 mmHg, which applies to adults breathing room air; the gradient normally widens on supplemental oxygen, so interpret results at high FiO₂ with care. This tool is for clinicians and students and does not replace clinical assessment.
With the default inputs, the a–a gradient is 9.7 mmHg. Change any value above to recalculate instantly.
How to use the a-a gradient calculator
- 1Enter the FiO₂ the patient was breathing when the blood gas was drawn.
- 2Enter PaO₂ and PaCO₂ from the arterial blood gas in mmHg (multiply kPa by 7.5).
- 3Enter the patient’s age; adjust barometric pressure at altitude.
- 4Compare the A–a gradient with the expected value for age.
Formula and method
The alveolar gas equation estimates the oxygen pressure in the alveoli. Inspired oxygen pressure is FiO₂ multiplied by barometric pressure minus water vapour pressure (47 mmHg at 37 °C); the PaCO₂ divided by the respiratory quotient (0.8) accounts for the oxygen displaced by carbon dioxide. Subtracting the measured arterial PaO₂ gives the gradient.
In healthy young adults on room air the gradient is about 5–10 mmHg and it widens with age because of increasing ventilation/perfusion inequality. Mellemgaard’s 1966 study of healthy subjects documented this rise with age; the widely taught bedside rule age ÷ 4 + 4 is a convenient approximation of the upper limit of normal on room air rather than an exact published regression, so treat values close to it as borderline. The PaO₂/FiO₂ ratio (used in ARDS definitions) and the a/A ratio are less affected by FiO₂ and are shown for context.
- PAO₂
- Alveolar oxygen partial pressure (mmHg)
- PaO₂, PaCO₂
- Arterial oxygen and carbon dioxide partial pressures (mmHg)
- FiO₂
- Fraction of inspired oxygen (0.21 on room air)
- Patm
- Barometric pressure (760 mmHg at sea level)
- PH₂O
- Water vapour pressure, 47 mmHg at body temperature
- RQ
- Respiratory quotient, usually 0.8
Worked examples
Healthy 40-year-old on room air
PAO₂ = 0.21 × (760 − 47) − 40 ÷ 0.8 = 149.73 − 50 = 99.73 mmHg. With a PaO₂ of 90 the gradient is 9.7 mmHg, below the expected 40 ÷ 4 + 4 = 14 mmHg, so gas exchange is normal.
Pulmonary embolism suspected, age 60
PAO₂ = 149.73 − 32 ÷ 0.8 = 109.73 mmHg, so the gradient is 109.73 − 65 = 44.7 mmHg — far above the expected 19 mmHg for a 60-year-old, consistent with a V/Q problem.
Opioid hypoventilation, age 28
PAO₂ = 149.73 − 70 ÷ 0.8 = 62.23 mmHg. The gradient is only 2.2 mmHg, so the low PaO₂ is explained entirely by hypoventilation rather than lung disease.
Frequently asked questions
What is a normal A-a gradient?+
On room air a normal gradient is roughly 5–10 mmHg in young adults and rises with age. A common estimate of the upper limit is age ÷ 4 + 4 mmHg, so about 14 mmHg at 40 and 24 mmHg at 80.
What causes an elevated A-a gradient?+
A raised gradient means oxygen is not moving efficiently from alveoli to blood. Causes include ventilation/perfusion mismatch (pneumonia, COPD, pulmonary embolism), right-to-left shunt and diffusion problems such as interstitial lung disease.
What causes hypoxemia with a normal A-a gradient?+
Hypoventilation (for example from opioids, sedatives or neuromuscular weakness) and low inspired oxygen at high altitude both lower PaO₂ while leaving the gradient normal, because the lungs themselves transfer oxygen normally.
Does the A-a gradient change with oxygen therapy?+
Yes. The gradient increases as FiO₂ rises, even in healthy lungs, so age-based normal values only apply on room air. At high FiO₂ the PaO₂/FiO₂ ratio or a/A ratio is often more useful.
How do I convert kPa to mmHg?+
Multiply kilopascals by 7.5 to get mmHg. For example, a PaO₂ of 12 kPa is 90 mmHg and a PaCO₂ of 5.3 kPa is about 40 mmHg.
For healthcare professionals and education only. This calculator implements a published formula or score but is not a diagnosis and does not replace clinical judgment. Verify inputs and results against the original source before using them in patient care.