We investigate the extent to which the Wilson-Bappu relationship holds for chromospherically active binaries using the Mg\,{\sc ii}~h\&k lines of 41 RS CVn stars observed with IUE. The resulting fits are different from the relationships obtained for single, less active stars. The parallax used were those from the {\sc hipparcos} catalogue, these give a much better correlation than the magnitudes taken from CABS. Within a particular luminosity class the relationship is good, however it tends to break down when we incorporate objects ranging in luminosity from class {\sc i} to {\sc v}. From model calculations there is very little dependence of the Mg\,{\sc ii} line width on effective temperature. The line width does however depend on the column mass at the transition region boundary showing increased line width at lower column mass. There is also a dependence on the column mass adopted for the temperature minimum, however, the major and dominant parameter is the surface gravity scaling as $g^{-1/4}$. Within a luminosity class more active objects will show larger lines widths reflecting a higher column mass deeper in the atmosphere, e.g. at the temperature minimum level. \keywords{Wilson-Bappu effect --- Mg\,{\sc ii} h\&k lines --- stellar chromospheres --- column mass}