ROX index: how to calculate (SpO2/FiO2) ÷ respiratory rate
The ROX index is the SpO2/FiO2 ratio divided by the respiratory rate. For a patient with an SpO2 of 95% on room air (FiO2 0.21) breathing 20 times a minute, ROX = (95 ÷ 0.21) ÷ 20 = 22.62.
Not a medical device. Not a diagnosis or dosing recommendation.
What is the ROX index?
ROX stands for respiratory rate–oxygenation. It joins two bedside observations in one number: how well oxygenated the patient is for the oxygen they're receiving (SpO2 divided by FiO2), and how fast they're breathing. Better oxygenation raises the index, and faster breathing lowers it.
Roca and colleagues described it in 2016 in patients with pneumonia receiving high-flow nasal cannula (HFNC) oxygen. It's also called the Roca ROX index or the HFNC ROX index.
This page explains the arithmetic. It doesn't give a cutoff, and it doesn't say what a value means for a patient.
The ROX index formula
rox = (spo2_percent / fio2) / respiratory_rateIn words: divide the SpO2 percent by the inspired oxygen fraction, then divide that result by the respiratory rate. Magent's calculator reports the index to 2 decimal places.
What each part means
| Term | Plain-English meaning | Unit | Accepted range |
|---|---|---|---|
spo2_percent | Oxygen saturation by pulse oximetry | % | 50–100 |
fio2 | Fraction of inspired oxygen | fraction, not percent | 0.21–1.0 |
respiratory_rate | Breaths per minute | breaths/min, whole number | 4–80 |
rox | (SpO2 ÷ FiO2) ÷ respiratory rate | index, no unit | 2 decimal places |
How the formula works
- Take the SpO2 as a percent, for example 95.
- Write FiO2 as a fraction: room air is 0.21, and 100% oxygen is 1.0.
- Divide SpO2 by FiO2. This is the SpO2/FiO2 (S/F) ratio.
- Divide the S/F ratio by the respiratory rate.
- Round to 2 decimal places.
The same SpO2 can give very different indexes. An SpO2 of 95% on room air gives an S/F ratio of 452.38…; the same 95% on an FiO2 of 1.0 gives 95. At a respiratory rate of 20, those become 22.62 and 4.75.
Units
FiO2 goes in as a fraction between 0.21 and 1.0, not as a percent. Entering a percent instead of a fraction would be rejected, because it's outside the accepted range. SpO2 goes in as a percent, not a fraction. The respiratory rate is a whole number of breaths per minute.
Worked examples
These use Magent's own expected values for the calculator.
Example 1: SpO2 95%, FiO2 0.21, rate 20
- S/F ratio: 95 ÷ 0.21 = 452.38…
- ROX: 452.38… ÷ 20 = 22.619… → 22.62
Example 2: SpO2 95%, FiO2 1.0, rate 20
- S/F ratio: 95 ÷ 1.0 = 95
- ROX: 95 ÷ 20 = 4.75
Example 3: SpO2 95%, FiO2 0.21, rate 24
- S/F ratio: 452.38…
- ROX: 452.38… ÷ 24 = 18.849… → 18.85
Example 4: SpO2 88%, FiO2 1.0, rate 32
- S/F ratio: 88 ÷ 1.0 = 88
- ROX: 88 ÷ 32 = 2.75
Examples 1 and 3 differ by respiratory rate alone: four more breaths a minute lowers the index from 22.62 to 18.85.
ROX index reference table
These values are computed from the formula with SpO2 fixed at 95% and rounded to 2 decimals, as the calculator reports them. They show how the index moves; they aren't targets, reference ranges or categories.
| Breaths/min \ FiO2 | 0.21 | 0.3 | 0.5 | 0.6 | 1.0 |
|---|---|---|---|---|---|
| 15 | 30.16 | 21.11 | 12.67 | 10.56 | 6.33 |
| 20 | 22.62 | 15.83 | 9.50 | 7.92 | 4.75 |
| 25 | 18.10 | 12.67 | 7.60 | 6.33 | 3.80 |
| 30 | 15.08 | 10.56 | 6.33 | 5.28 | 3.17 |
| 35 | 12.93 | 9.05 | 5.43 | 4.52 | 2.71 |
Moving right along a row (more oxygen for the same saturation) lowers the index; so does moving down a column (faster breathing).
History of the ROX index
The index comes from O. Roca and colleagues, Predicting success of high-flow nasal cannula in pneumonia patients with hypoxemic respiratory failure: The utility of the ROX index, published in the Journal of Critical Care in 2016 (volume 35, pages 200–205).
The abstract describes a four-year prospective observational cohort at two centers, including 157 patients with severe pneumonia treated with HFNC. It defines the ROX index as the ratio of pulse oximetry/fraction of inspired oxygen to respiratory rate. Of those patients, 44 eventually required mechanical ventilation. The authors reported the index's accuracy after 12 hours of HFNC.
When it's used
A 2022 meta-analysis describes ROX as a newer index for predicting the outcome of high-flow nasal cannula therapy in adults.[1] The studies it pooled measured the index at different times after HFNC started, and the time of measurement was one of the factors the authors examined.[1]
Where it's used
The pooled studies included patients with pneumonia and acute respiratory failure from other causes.[1] All the inputs are bedside readings: a pulse-oximeter saturation, the set oxygen fraction, and a counted respiratory rate.
Who uses it
The same meta-analysis notes that studies defined HFNC failure differently and lacked common intubation criteria, which may cause practice variation among the clinicians using the index.[1]
Limits of the calculation
- It's a ratio of bedside readings. It isn't a ventilation order and doesn't classify the result.
- The calculator doesn't apply any time-based cut-point from the 2016 paper; in that study the timing of the measurement mattered.
- It isn't the PaO2/FiO2 (P/F) ratio, which uses arterial blood gas, not pulse oximetry.
- It isn't the rapid shallow breathing index, which divides respiratory rate by tidal volume.
- Inputs outside the accepted ranges are rejected, not estimated. FiO2 must be a fraction and the rate a whole number.
Clinical decisions belong to a qualified clinician who knows the patient.
How it differs from related calculators
- SpO2/FiO2 ratio is the first step of ROX on its own, without the respiratory rate.
- PaO2/FiO2 ratio divides arterial PO2 in mm Hg by FiO2.
- Rapid shallow breathing index divides respiratory rate by tidal volume in liters; ROX divides by respiratory rate instead.
Glossary
- SpO2: oxygen saturation measured by a pulse oximeter, as a percent.
- FiO2: fraction of inspired oxygen, from 0.21 (room air) to 1.0.
- S/F ratio: SpO2 divided by FiO2.
- High-flow nasal cannula (HFNC): heated, humidified oxygen delivered at high flow through nasal prongs.
- Respiratory rate: breaths per minute.
Common mistakes
- Entering FiO2 as a percent. Enter it as a fraction between 0.21 and 1.0, not as a percent.
- Entering SpO2 as a fraction. Use the percentage, not a fraction.
- Dividing in the wrong order. Divide SpO2 by FiO2 first, then divide by the rate. Multiplying by the rate gives a different number.
- Confusing ROX with P/F. ROX uses pulse oximetry; P/F uses an arterial PO2.
Source
Roca O, Messika J, Caralt B, García-de-Acilu M, Sztrymf B, Ricard JD, Masclans JR. Predicting success of high-flow nasal cannula in pneumonia patients with hypoxemic respiratory failure: The utility of the ROX index. J Crit Care. 2016;35:200-205. DOI: 10.1016/j.jcrc.2016.05.022
Further reading
- Junhai Z, Jing Y, Beibei C, Li L. The value of ROX index in predicting the outcome of high flow nasal cannula: a systematic review and meta-analysis. Respir Res. 2022;23:33.
Frequently asked questions
How do you calculate the ROX index?
Divide SpO2 by FiO2, then divide by the respiratory rate. For 95%, 0.21 and 20 breaths a minute, that's (95 ÷ 0.21) ÷ 20 = 22.62.
What is a good ROX index?
This page doesn't give a cutoff. It calculates the index; in the original study the timing of the measurement mattered, and what a value means depends on the clinical context.
What does ROX stand for?
Respiratory rate–oxygenation. It combines the SpO2/FiO2 ratio with the respiratory rate.
Is FiO2 entered as a percent or a decimal?
As a decimal fraction between 0.21 and 1.0. Room air is 0.21.
Is the ROX index the same as the S/F ratio?
No. The S/F ratio is SpO2 ÷ FiO2. ROX divides that ratio by the respiratory rate.
Who developed the ROX index?
O. Roca and colleagues, in a 2016 paper in the Journal of Critical Care.