How do you calculate the P/F ratio?
Divide the arterial PaO₂ in mmHg by the FiO₂ written as a fraction. On its own a PaO₂ says little: 80 mmHg is reassuring on room air and worrying on 80% oxygen. Dividing by the FiO₂ puts both situations on the same scale.
P/F ratio = PaO₂ (mmHg) ÷ FiO₂ (as a fraction)
If the PaO₂ is in kPa it is converted first:
PaO₂ (mmHg) = PaO₂ (kPa) × 7.50062
The calculator also divides the final ratio by 7.50062 to show it in kPa.
How to use the calculator
- Choose the PaO₂ unit your blood gas analyser uses: mmHg or kPa.
- Enter the PaO₂ from the arterial sample.
- Enter the FiO₂ at the moment the sample was taken, as a percentage (21–100) or a fraction (0.21–1).
- Read the P/F ratio in mmHg, rounded to a whole number, with the Berlin band and the value In kPa.
- In the working, the kPa step shows the factor rounded to 7.501, but the calculation uses the full 7.50062.
Worked examples
Example 1 – exactly on a cut-off. PaO₂ 80 mmHg on FiO₂ 40%. FiO₂ as a fraction = 0.4. 80 ÷ 0.4 = 200 mmHg (26.7 kPa). Berlin band: Moderate (100–200). A ratio of exactly 200 is moderate, because mild starts above 200.
Example 2 – PaO₂ in kPa. PaO₂ 12 kPa on FiO₂ 0.6. 12 × 7.50062 = 90 mmHg. 90 ÷ 0.6 = 150 mmHg (20 kPa). Berlin band: Moderate (100–200).
Example 3 – high oxygen requirement. PaO₂ 60 mmHg on FiO₂ 80%. 60 ÷ 0.8 = 75 mmHg (10 kPa). Berlin band: Severe (≤ 100). For comparison, a PaO₂ of 95 mmHg on room air (0.21) gives 452 mmHg: Above 300, with no warning.
Berlin ARDS oxygenation bands
| Band shown | P/F in mmHg | P/F in kPa (approx.) |
|---|---|---|
| Above 300 | above 300 | above 40 |
| Mild (200–300) | above 200, up to 300 | 26.7–40 |
| Moderate (100–200) | above 100, up to 200 | 13.3–26.7 |
| Severe (≤ 100) | 100 or less | 13.3 or less |
The band is set on the ratio shown, rounded to a whole number, so the label always matches the screen. In the Berlin definition the mild band applies with PEEP or CPAP of at least 5 cmH₂O, and the moderate and severe bands with PEEP of at least 5 cmH₂O. Each applies only when the other criteria (timing, imaging, origin of the oedema) are met. When the ratio is 300 or below, the calculator shows this reminder.
Common mistakes
- Using the wrong FiO₂. You need the FiO₂ being delivered when the blood was drawn. If the oxygen was turned up just before the sample, the ratio describes the new setting, not the old one.
- Mixing up mmHg and kPa. A PaO₂ of 12 entered as mmHg instead of kPa gives a ratio about 7.5 times too low.
- Using a venous or capillary sample. The ratio is defined for arterial PaO₂. Venous oxygen tension is much lower and gives a meaningless result.
- Treating the band as a diagnosis. A low ratio describes impaired oxygenation; whether it is ARDS depends on the rest of the clinical picture.
Limits
The P/F ratio ignores the ventilator settings. The same ratio can come with very different PEEP levels, and changing the PEEP alone can move a patient from one band to another. The link between FiO₂ and PaO₂ is not linear, so the ratio can shift simply because the FiO₂ was changed. Altitude, the accuracy of the delivered FiO₂ and the timing of the sample all affect the number.
To place the P/F ratio in a full blood gas reading, see the arterial blood gas guide. In the deteriorating patient, the mean arterial pressure and the qSOFA score complete the picture.
Frequently asked questions
What is a normal P/F ratio?
Roughly 400 to 500 mmHg in a healthy adult breathing room air at sea level: a PaO₂ of about 90 to 100 mmHg divided by 0.21. Values fall with age and at altitude. A ratio of 300 or less marks impaired oxygenation, the range the Berlin bands describe.
Do I enter FiO₂ as 40 or 0.4?
Either works. Any value above 1 is read as a percentage and divided by 100, so 40 and 0.4 give the same result. Values outside 21–100% are rejected with an error message. Room air is 21%, or 0.21 as a fraction.
My blood gas reports PaO₂ in kPa. What changes?
Select kPa as the PaO₂ unit; nothing else changes. The calculator converts to mmHg by multiplying by 7.50062, calculates the ratio, and also shows it in kPa. The Berlin cut-offs of 300, 200 and 100 mmHg correspond to about 40, 26.7 and 13.3 kPa.
Does a P/F ratio under 300 mean the patient has ARDS?
No. The ratio measures how well oxygen is being transferred, whatever the cause. The Berlin definition also requires onset within a week, bilateral opacities on imaging not fully explained by other causes, respiratory failure not fully explained by heart failure or fluid overload, and PEEP of at least 5 cmH₂O (for the mild band, CPAP of at least 5 cmH₂O also counts).
Is the P/F ratio the same as the Horowitz index?
Yes. PaO₂/FiO₂ ratio, P/F ratio and Horowitz index are different names for the same calculation. Horowitz is the name more common in German- and Italian-speaking countries, while English-language papers usually write PaO₂/FiO₂ or P/F. The numbers and the cut-offs are identical.
Can I estimate FiO₂ for a patient on nasal cannula?
Only roughly. With low-flow devices the delivered FiO₂ depends on breathing pattern and minute ventilation, so any estimate is uncertain. The resulting P/F ratio is much less reliable than one taken on a ventilator or a high-flow system with a set FiO₂, so it’s worth recording the device next to the result.
What is the newer global definition of ARDS?
A 2023 consensus update that keeps the Berlin oxygenation bands but broadens the criteria. It accepts patients on high-flow nasal oxygen of at least 30 L/min and allows an SpO₂/FiO₂ ratio of 315 or less when no blood gas is available. This calculator works only with PaO₂.