SOFA Score — SpO₂-Imputed P:F Ratio

Respiratory component derived from SpO₂ + O₂ device
in place of measured PaO₂
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For education / workflow use only — not a substitute for an arterial blood gas. Imputation error grows as SpO₂ approaches 100% (flat top of the oxyhemoglobin curve) and at SpO₂ < 80% (curve becomes unstable). Obtain a real ABG whenever one is available or the patient is trending toward moderate–severe hypoxemia.

Step 1 — Oxygenation

Imputes PaO₂ from SpO₂ (Ellis solution to the Severinghaus equation), estimates FiO₂ from the delivery device, then computes PaO₂:FiO₂.

Pulse oximetry reading, room air or on O₂
Respiratory support (mechanical ventilation, incl. CPAP)?
Required for a respiratory score of 3 or 4
Estimated FiO₂
21%
Imputed PaO₂
–
Imputed PaO₂ : FiO₂ ratio
–
SpO₂ in this range makes the imputation unreliable — obtain an arterial blood gas.
P:F < 200 but no respiratory support recorded — respiratory points are capped at 2.
Methodology & sources

1. SpO₂ → PaO₂ — Ellis's closed-form inversion of the Severinghaus oxyhemoglobin dissociation equation (Ellis RK, J Appl Physiol 1989;67(2):902), the same method used by Open Critical Care's Imputed PaO₂ from SpO₂ Calculator. Given S = SpO₂ as a fraction:

B = 23400 · S / (1 − S) x = ∛(B/2 + √((B/2)² + 125000)) − ∛(√((B/2)² + 125000) − B/2) PaO₂ (mmHg) = x

SpO₂ readings of 100% are treated as 99.6% before imputation, since the equation is undefined at S = 1.

2. Device + flow → FiO₂ — standard clinical low-flow approximation (≈4% FiO₂ per L/min above room air for nasal cannula), consistent with the estimation tables referenced in MDCalc's SOFA score evidence section:

Nasal cannula: FiO₂ = 0.21 + 0.04 × flow (L/min), capped at 0.44 Simple face mask: 0.35–0.60 (mapped from 5–10 L/min) Non-rebreather: 0.60–0.90+ (mapped from 10–15 L/min) HFNC / vent / CPAP: set directly (device controls FiO₂)

3. P:F ratio → SOFA respiratory points — thresholds per the original SOFA respiratory criterion (MDCalc, SOFA score):

≥ 400 mmHg .......................... 0 < 400 mmHg .......................... 1 < 300 mmHg .......................... 2 < 200 mmHg + respiratory support ... 3 < 100 mmHg + respiratory support ... 4

Step 2 — Remaining SOFA parameters

Use the most abnormal value over the assessment period (typically 24 h).

×10³/µL and ×10⁹/L are numerically identical — switching units only changes the label, the number stays the same.
If sedated, estimate the GCS the patient would have off sedation
Total SOFA score
0/24
Respiratory pts from
–

Subscores by organ system

SystemBasisPts
RespiratoryPaO₂:FiO₂ –0
CoagulationPlatelets –0
LiverBilirubin –0
CardiovascularNo hypotension0
CNSGCS –0
RenalCreatinine –0

Reference — SOFA respiratory criterion

PaO₂:FiO₂Pts
≥ 400 mmHg—0
< 400 mmHg—1
< 300 mmHg—2
< 200 mmHg+ ventilatory support3
< 100 mmHg+ ventilatory support4