What this calculator does
The A-a gradient compares the oxygen that should be in the alveoli against what actually reaches the blood. A small gap is normal; a large one means oxygen is not crossing properly, which narrows the cause of hypoxaemia considerably.
What counts as large depends on age. The expected gradient is roughly age over four plus four, so a gradient of 4.7 mmHg is unremarkable at any age, while a gradient near 40 would be well outside the expected range for a 30 year old.
The formula
Alveolar oxygen is inspired fraction times the dry barometric pressure of 713 mmHg, less carbon dioxide divided by the respiratory quotient. The measured arterial oxygen is then subtracted.
| Term | Meaning |
|---|---|
| A-a gradient | The difference between calculated alveolar and measured arterial oxygen. |
| Alveolar gas equation | The calculation that produces the alveolar figure from FiO2 and PaCO2. |
| Expected gradient | Roughly age divided by four plus four, since the gap widens normally with age. |
The inputs explained
| Field | What to enter |
|---|---|
| FiO₂ (%) | Fraction of inspired oxygen as a percentage. Room air is 21. |
| Arterial PaCO₂ (mmHg) | Arterial PaCO2 in mmHg, which reduces alveolar oxygen. |
| Arterial PaO₂ (mmHg) | Arterial PaO2 in mmHg, subtracted from the alveolar figure. |
| Age (years) | Age in years, used only for the expected gradient comparison. |
When to use it
Working out why someone is hypoxaemic
A normal gradient points toward hypoventilation; a raised one toward a gas exchange problem.
Assessing a blood gas
The gradient adds information that PaO2 alone does not carry.
Adjusting for age
A gradient that is normal at 80 would be abnormal at 20.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the expected gradient change with age?
The same blood gas assessed at three ages.
| Age | A-a gradient | Expected gradient for age |
|---|---|---|
| 20 years | 4.7 mmHg | 9.0 mmHg |
| 50 years | 4.7 mmHg | 16.5 mmHg |
| 80 years | 4.7 mmHg | 24.0 mmHg |
Questions
What does a normal gradient with low oxygen mean?
That the alveolar oxygen is itself low, which usually points to hypoventilation or a low inspired oxygen fraction rather than a problem crossing into the blood. That distinction is the main reason to calculate the gradient.
Why does the gradient widen with age?
Because the match between ventilation and blood flow becomes less uniform as the lungs age. It is a normal change, which is why the comparison is against an age-adjusted expectation.
Where does 713 come from?
It is standard atmospheric pressure of 760 mmHg less the water vapour pressure of 47 mmHg, since inspired air is fully humidified by the time it reaches the alveoli. At altitude the barometric figure is lower.
Is the gradient reliable on supplemental oxygen?
Less so. It was characterised on room air, and on high inspired fractions the expected values shift, so many clinicians prefer the PaO2/FiO2 ratio in that situation.
For the oxygenation index on supplemental oxygen, see the PaO2/FiO2 ratio calculator. For expected lung volume, see the predicted vital capacity calculator.