Another important equation in chromatographic separations is the fundamental resolution equation. The equation relates the resolution of two compounds (RS) to the number of theoretical plates ($$N$$), retention or capacity factor ($$k$$), and selectivity factor ($$\alpha$$). Appendix I shows the derivation of the fundamental resolution equation. Since we would usually be interested in separating two compounds that are close to each other in a chromatogram, and therefore possibly not resolved, we usually think of applying this equation when we want to improve the resolution of two adjacent components.
$\mathrm{R_S = \left( \dfrac{\sqrt{N}}{4}\right ) \left( \dfrac{\alpha -1}{\alpha}\right ) \left( \dfrac{k _2}{1 + k_2}\right )}$