Oxygenation ratio ($P_{\mathrm{a}{O}_2}/F_{\mathrm{I}{O}_2}$)

The oxygenation ratio, often called the P/F ratio, divides arterial oxygen partial pressure by inspired oxygen fraction:The denominator is a fraction, not a percentage number. Since it is dimensionless, the ratio retains the pressure units used in the numerator. An arterial blood gas analysis provides the partial-pressure measurement; its measurement target differs from oxygen saturation.^[ref]

For a constructed example, $P_{\mathrm{a}{O}_2}=75\mathrm{mmHg}$ and $F_{\mathrm{I}{O}_2}=0.50$ give $R=150\mathrm{mmHg}$, approximately $20.0\mathrm{kPa}$. Dividing by $50$ instead would give a result 100 times too small. Values expressed in kilopascals cannot be compared numerically with values expressed in millimeters of mercury without unit conversion.

The 2012 Berlin definition used this ratio in characterizing acute respiratory distress syndrome. That historical consensus also considered other syndrome criteria; the ratio alone does not establish the syndrome.^[ref] The inspired fraction and respiratory-support conditions must be recorded alongside the arterial measurement. Changing the denominator is not an experiment showing that arterial partial pressure must change proportionally.

A first-order uncertainty propagation calculation shows why both measurements matter:If independent standard uncertainties are stipulated as $3\mathrm{mmHg}$ and $0.02$ for the example above, each relative uncertainty is $0.04$. Their quadratic combination gives a relative standard uncertainty $\sqrt{0.04^2+0.04^2}\approx 0.0566$, or about $8.5\mathrm{mmHg}$ in the ratio. This example concerns measurement arithmetic, not a diagnostic threshold.