= Chromatographic resolution
{title2=$R_s$}
<Chromatographic resolution> measures the separation of two peaks relative to their widths. With <chromatographic retention times> $t_{R2}>t_{R1}$ and baseline widths $w_{b1},w_{b2}$, its conventional definition is
$$
R_s=\frac{2(t_{R2}-t_{R1})}{w_{b1}+w_{b2}}.
$$
The numerator and denominator have the same units, so $R_s$ is dimensionless. A large time difference does not by itself imply good separation if both peaks are correspondingly broad.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book) by International Union of Pure and Applied Chemistry>[Peak resolution, entryP04465: average baseline-width definition]{ref}
For an original example, peaks at $4.0$ and $4.6$ minutes, each $0.40$ minutes wide at the base, have $R_s=2(0.6)/(0.8)=1.5$. If their widths increase to $0.60$ minutes while their peak times stay fixed, $R_s=1$. Measuring only the peak centers would miss the deterioration.
Simply rescaling the time axis cannot change <chromatographic resolution>. If all times and widths in the first example double, then $R_s=2(1.2)/(1.6)=1.5$ again. This is a statement about a rescaled trace, not a claim that changing the flow of a real column leaves its separation physics unchanged.
The peak-width convention must be stated. Half-height widths are smaller than baseline widths and cannot be substituted into the same formula without the corresponding conversion. Peak asymmetry, overlapping components and unequal signal strengths can also make a single reported $R_s$ an incomplete account of whether a particular quantitative measurement is reliable.
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