What this calculator does
Alveolar-arterial (A-a) gradient works out gap between calculated and measured arterial oxygen, a clue to the cause of hypoxaemia. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaPAO2 = FiO2 × (760 − 47) − PaCO2 / 0.8; A-a gradient = PAO2 − PaO2; expected gradient ≈ age/4 + 4
The inputs explained
| Field | What to enter |
|---|---|
| FiO₂ (%) | A number, measured in %. Starts at 21. |
| Arterial PaCO₂ (mmHg) | A number, measured in mmHg. Starts at 40. |
| Arterial PaO₂ (mmHg) | A number, measured in mmHg. Starts at 95. |
| Age (years) | A number, measured in years. Starts at 30. |
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 the answer changes with fio₂
Every other input is held at the calculator’s starting values while fio₂ varies. Select any row to load that scenario into the calculator.