What the A–a gradient measures
Oxygen travels from the air in the lungs’ tiny air sacs, the alveoli, into the blood. The alveolar–arterial (A–a) gradient compares the oxygen pressure that should be in the alveoli with the oxygen pressure actually measured in arterial blood. A small difference is normal; a large one means oxygen is not crossing efficiently, which points to a problem inside the lungs.
The alveolar gas equation
The alveolar oxygen pressure cannot be measured directly, so it is calculated:
PAO₂ = FiO₂ × (Patm − PH₂O) − PaCO₂ ÷ RQ
- FiO₂: fraction of inspired oxygen, 0.21 on room air
- Patm: atmospheric pressure, 760 mmHg at sea level
- PH₂O: water vapor pressure at body temperature, 47 mmHg
- PaCO₂: arterial carbon dioxide from the blood gas
- RQ: respiratory quotient, usually taken as 0.8
Then A–a gradient = PAO₂ − PaO₂.
Worked example
A 40-year-old breathing room air has a PaO₂ of 90 mmHg and a PaCO₂ of 40 mmHg.
- PAO₂ = 0.21 × (760 − 47) − 40 ÷ 0.8 = 149.7 − 50 = 99.7 mmHg
- A–a gradient = 99.7 − 90 = 9.7 mmHg
- Expected upper limit for age = 40 ÷ 4 + 4 = 14 mmHg: normal
- P/F ratio = 90 ÷ 0.21 ≈ 429
Now a patient with pneumonia on 40% oxygen, with a PaO₂ of 70 and a PaCO₂ of 35: PAO₂ = 0.40 × 713 − 43.8 ≈ 241, so the gradient is about 171 mmHg and the P/F ratio 175, a clear gas-exchange problem.
Using the gradient to find the cause of low oxygen
| Gradient | Likely mechanism | Examples |
|---|---|---|
| Normal | Hypoventilation or low inspired oxygen | Opioid overdose, neuromuscular weakness, high altitude |
| High | V/Q mismatch | Pneumonia, asthma, COPD, pulmonary embolism |
| High, little response to oxygen | Shunt | ARDS, collapsed lung, intracardiac shunt |
| High | Diffusion limitation | Interstitial lung disease |
The P/F ratio
The PaO₂/FiO₂ ratio is simpler and less affected by the oxygen concentration. Under the Berlin definition of ARDS, with at least 5 cmH₂O of PEEP, 200–300 is mild, 100–199 moderate and below 100 severe.
Limits
- The normal range widens at higher FiO₂, so the age formula applies to room air.
- At altitude, enter the local barometric pressure: about 630 mmHg in Denver.
- The RQ of 0.8 is an assumption; it varies with diet and metabolism.
This calculator is for general information and education. It is not medical advice and does not replace the judgment of a doctor, nurse or pharmacist who knows the full clinical picture.