= Fractional oxyhemoglobin
{title2=$F_{\mathrm O_2\mathrm{Hb}}$}
\b[Fractional oxyhemoglobin] is the <oxyhemoglobin> concentration divided by the concentration of all measured <hemoglobin> species in the same <blood> sample. With $H_O,H_D,H_C,H_M$ denoting <oxyhemoglobin>, <deoxyhemoglobin>, <carboxyhemoglobin> and <methemoglobin> concentrations, respectively,
$$
F_{\mathrm O_2\mathrm{Hb}}=\frac{H_O}{H_O+H_D+H_C+H_M}.
$$
Additional measured <hemoglobin> species belong in the denominator when present. <Functional oxygen saturation> instead uses $H_O/(H_O+H_D)$. The distinction is the denominator, not whether the result is written as a <fraction> or a <percentage>.<Oxyhemoglobin by Radiometer>[Definition and “FO2Hb versus oxygen saturation (sO2)”]{ref}
For a constructed mixture with concentrations proportional to $85,5,10,0$, respectively, <fractional oxyhemoglobin> is $85\%$, while <functional oxygen saturation> is $85/90\approx94.4\%$. The second number excludes the <carboxyhemoglobin> from its denominator; it has not created additional oxygen-carrying <oxyhemoglobin>.
This distinction matters when converting <hemoglobin> measurements into <arterial oxygen content>. If $H$ is total <hemoglobin> concentration and $\beta$ is a stipulated oxygen-binding capacity per unit <hemoglobin> mass, the bound-oxygen term is $\beta HF_{\mathrm O_2\mathrm{Hb}}$. Choosing $H=15$ g/dL and $\beta=1.34$ mL/g in the example gives $17.085$ mL of bound <oxygen> per dL of <blood>. Substituting $85/90$ instead would give about $18.98$ mL/dL. This calculation isolates the denominator error; dissolved <oxygen> is a separate contribution. A measurement of <oxygen saturation> alone therefore does not determine total <blood> oxygen content.
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