Hong Life CalculatorsUnderstanding the A-a gradient and P/F ratio calculator — concept and principle
The alveolar–arterial (A-a) oxygen gradient compares the oxygen pressure expected in the lungs' air sacs with the oxygen actually measured in arterial blood. The P/F ratio divides arterial oxygen by the inspired oxygen fraction. Together they help clinicians work out why a patient has low blood oxygen and how severe a lung problem is, for example in pneumonia or acute respiratory distress syndrome (ARDS).
How it is calculated
PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ ÷ 0.8
A-a gradient = PAO₂ − PaO₂
P/F ratio = PaO₂ ÷ FiO₂ (FiO₂ as a fraction, e.g. 0.21)
- FiO₂ entered as a percentage; room air is 21%.
- Patm is barometric pressure, 760 mmHg at sea level; 47 mmHg is water vapour pressure at 37 °C.
- 0.8 is the assumed respiratory quotient.
- Expected A-a gradient on room air ≈ age ÷ 4 + 4.
The principle
The alveolar gas equation describes what happens to inspired air: it is humidified, which dilutes the oxygen, and in the alveoli oxygen is taken up while carbon dioxide is added. In healthy lungs the arterial oxygen is only slightly below the alveolar value. A wide gap means oxygen is not getting from air sacs into blood, because of ventilation–perfusion mismatch, shunt or diffusion problems. If the gradient is normal but PaO₂ is low, the cause is hypoventilation or low inspired oxygen, such as at altitude.
Worked example
- FiO₂ × (760 − 47) = 0.21 × 713 = 149.73.
- PaCO₂ ÷ 0.8 = 40 ÷ 0.8 = 50.
- PAO₂ = 149.73 − 50 = 99.73 mmHg.
- A-a gradient = 99.73 − 90 = 9.73 mmHg; expected for age 35 = 35 ÷ 4 + 4 = 12.75, so it is normal.
- P/F ratio = 90 ÷ 0.21 = 428.6, shown as 429, in the > 300 category.
| Barometric pressure (mmHg) | A-a gradient |
|---|---|
| 190 | -109.97 |
| 380 | -70.07 |
| 570 | -30.17 |
| 760 | 9.73 |
| 950 | 49.63 |
| 1,140 | 89.53 |
| 1,520 | 169.33 |
How to read the result
A normal gradient on room air is usually below about 10–15 mmHg in young adults and increases with age. A raised gradient points to lung or circulation problems such as pneumonia, pulmonary embolism or oedema. A P/F ratio above 300 is normal or near normal. Under the Berlin definition of ARDS, with PEEP of at least 5 cmH₂O and other criteria met, 200–300 is mild, 100–200 moderate and 100 or below severe.
Common mistakes
- Applying the age rule on supplemental oxygen; the gradient widens as FiO₂ rises.
- Forgetting to lower Patm at altitude.
- Labelling ARDS from the P/F ratio alone; timing, imaging and the cause of oedema are also required.
Frequently asked questions
What is a normal A-a gradient?
Roughly age ÷ 4 + 4 mmHg on room air.
What is a normal P/F ratio?
On room air it is usually around 400–500 in healthy people.
Why use 47 mmHg?
It is the water vapour pressure at body temperature, which takes up part of the total gas pressure in the airways.
Sources: ARDS Definition Task Force. Acute respiratory distress syndrome: the Berlin Definition. JAMA 2012. · West JB. Respiratory Physiology: The Essentials. Wolters Kluwer.