= Oxygenation ratio
{title2=$P_{\mathrm a O_2}/F_{\mathrm I O_2}$}
The \b[oxygenation ratio], often called the P/F ratio, divides <arterial oxygen partial pressure> by <inspired oxygen fraction>:
$$
R=\frac{P_{\mathrm a O_2}}{F_{\mathrm I O_2}}.
$$
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>.<Arterial Blood Gas (ABG) Test by MedlinePlus>[What is an arterial blood gas test?: oxygen partial pressure and 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.<Acute respiratory distress syndrome: the Berlin Definition by the ARDS Definition Task Force>[JAMA 307, 2526–2533: definition and performance evaluation]{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:
$$
\frac{dR}{R}=\frac{dP_{\mathrm a O_2}}{P_{\mathrm a O_2}}-\frac{dF_{\mathrm I O_2}}{F_{\mathrm I O_2}}.
$$
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 $\sqrt{0.04^2+0.04^2}\approx0.0566$, or about $8.5\,\mathrm{mmHg}$ in the ratio. This example concerns measurement arithmetic, not a diagnostic threshold.
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