The separation of two peaks in terms of their average peak width at base (t R2 > t R1): \[R_{\text{s}}=\frac{t_{\text{R2}}\,-\,t_{\text{R1}}}{\frac{w_{\text{b1}}\,+\,w_{\text{b2}}}{2}}=\frac{2\ (t_{\text{R2}}- t_{\text{R1}})}{w_{\text{b1}}\,+\,w_{\text{b2}}}\] In the case of two adjacent peaks it may be assumed that w b1 ≈ w b2, and thus, the width of the second peak may be substituted for the average value: \[R_{\text{s}}\approx \frac{t_{\text{R2}}\,-\,t_{\text{R1}}}{w_{\text{b2}}}\]
Sources:
Orange Book, 2nd ed., p. 108 (https://media.iupac.org/publications/analytical_compendium/)
PAC, 1993, 65, 819. 'Nomenclature for chromatography (IUPAC Recommendations 1993)' on page 847 (https://doi.org/10.1351/pac199365040819)