A–a gradient calculator
Enter the inspired oxygen, the blood gas PaO2 and PaCO2 and the patient's age to get the alveolar-arterial (A–a) oxygen gradient, the expected upper value for age and the P/F ratio. Works in mmHg or kPa. Information for clinicians, not a diagnosis.
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How to use it
- Choose mmHg or kPa, as your blood gas analyser reports.
- Enter FiO2 in percent (21 on room air), PaO2 and PaCO2 from the arterial gas.
- Change the atmospheric pressure if you are well above sea level.
- Enter the age to get the expected upper value.
How it works
- Alveolar oxygen: PAO2 = FiO2 × (Patm − 47) − PaCO2 ÷ 0.8, in mmHg.
- A–a gradient = PAO2 − PaO2.
- Expected upper value ≈ age ÷ 4 + 4 mmHg.
- P/F ratio = PaO2 (mmHg) ÷ FiO2 (as a fraction).
In kPa mode the inputs are converted with 1 kPa = 7.5006 mmHg and the results converted back.
Worked example
A 40-year-old on room air at sea level has PaO2 90 mmHg and PaCO2 40 mmHg.
PAO2 = 0.21 × (760 − 47) − 40 ÷ 0.8 = 149.73 − 50 = 99.7 mmHg. The gradient is 99.73 − 90 = 9.7 mmHg, below the expected 40 ÷ 4 + 4 = 14 mmHg. The P/F ratio is 90 ÷ 0.21 = 429.
On 50% oxygen a 60-year-old with PaO2 80 and PaCO2 40 has PAO2 = 0.5 × 713 − 50 = 306.5 mmHg, a gradient of 226.5 mmHg and a P/F ratio of 160.
Tips
- FiO2 from nasal cannulas or simple masks is only an estimate, so the gradient is approximate.
- The age formula is for room air; on extra oxygen a “normal” gradient is higher.
- Draw the gas at a steady state, at least several minutes after changing oxygen.
- The result is information and does not replace clinical judgment.
Frequently asked questions
What is a normal A–a gradient?
On room air it rises with age. A common estimate of the upper normal value is age ÷ 4 + 4 mmHg, so about 14 mmHg at 40 and 19 mmHg at 60. The gradient also rises when more oxygen is breathed, so the estimate fits room air best.
What does a raised gradient mean?
That oxygen is not getting from the alveoli into the blood as well as it should, as with pneumonia, pulmonary embolism, fluid in the lungs or a shunt. Low oxygen with a normal gradient points instead to hypoventilation or low inspired oxygen, for example at altitude.
How is the alveolar oxygen calculated?
With the alveolar gas equation: PAO2 = FiO2 × (atmospheric pressure − 47) − PaCO2 ÷ 0.8, in mmHg. 47 mmHg is water vapor pressure at body temperature and 0.8 is the assumed respiratory quotient.
What is the P/F ratio for?
PaO2 divided by FiO2 as a fraction is a quick measure of oxygenation. The Berlin definition of ARDS uses it with PEEP of at least 5 cmH2O: 201–300 mild, 101–200 moderate, 100 or less severe. A low ratio alone is not ARDS.