A-a Gradient Calculator (Alveolar-Arterial)
This A-a gradient calculator finds the alveolar-arterial oxygen gradient, the difference between the oxygen pressure in your alveoli (PAO2) and your arterial blood (PaO2). Enter FiO2, PaCO2, PaO2, and age, and it returns the gradient, the alveolar PO2, and the value expected for your age to help localise the cause of low blood oxygen.
Rates and fees change frequently. Always confirm the current figures
with the official authority before relying on this result.
- Sea-level barometric pressure assumed. Clinical reference only.
Formula
PAO2 = FiO2 × (760 − 47) − PaCO2 ÷ 0.8; A-a = PAO2 − PaO2
- The alveolar oxygen pressure is estimated with the alveolar gas equation: PAO2 = FiO2 × (Patm − PH2O) − PaCO2 / R, which at sea level becomes FiO2 × (760 − 47) − PaCO2 / 0.8.
- The A-a gradient is then PAO2 minus the measured arterial PaO2 from a blood gas.
- A normal gradient rises with age; a common rule of thumb for the upper limit on room air is (age / 4) + 4 mmHg.
- A widened gradient suggests a gas-exchange problem (V/Q mismatch, shunt, or diffusion defect), while a normal gradient with low PaO2 points to hypoventilation or low inspired oxygen.
- FiO2 is entered as a percentage (21% is room air); the result assumes sea-level barometric pressure.
Example Calculation
Inputs
- FiO2: 21 %
- PaCO2: 40 mmHg
- PaO2: 90 mmHg
- Age: 40 years
On room air (FiO2 21%) with PaCO2 = 40 and PaO2 = 90 mmHg, PAO2 = 0.21 × (760 − 47) − 40 / 0.8 ≈ 100 mmHg. The A-a gradient is about 100 − 90 = 10 mmHg, close to the ~14 mmHg expected for a 40-year-old.
Frequently asked questions
What is the A-a gradient?
It is the difference between the oxygen pressure in the alveoli (PAO2) and in arterial blood (PaO2). It measures how efficiently oxygen moves from the lungs into the blood.
What is a normal A-a gradient?
It varies with age and inspired oxygen. On room air a common estimate of the upper normal limit is (age / 4) + 4 mmHg, so it is roughly 5-15 mmHg in young adults.
What does a widened A-a gradient mean?
It suggests impaired gas exchange, such as V/Q mismatch, a right-to-left shunt, or a diffusion problem. A normal gradient with low oxygen instead points to hypoventilation or low FiO2.
Why does the calculator use 760 and 47?
760 mmHg is the barometric pressure at sea level and 47 mmHg is the water-vapour pressure at body temperature, which is subtracted to get the pressure of dry inspired gas.
Should I enter FiO2 as a percent or a fraction?
Enter it as a percentage (e.g. 21 for room air). The calculator converts it to a fraction internally before applying the alveolar gas equation.
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