  The connection between stellar rotation, stellar activity, and convective
turnover time is revisited with a focus on the sole contribution of magnetic
activity to the Ca II H&K emission, the so-called excess flux, and its
dimensionless indicator R$^{+}_{\rm{HK}}$ in relation to other stellar
parameters and activity indicators. Our study is based on a sample of 169
main-sequence stars with directly measured Mount Wilson S-indices and rotation
periods. The R$^{+}_{\rm{HK}}$ values are derived from the respective S-indices
and related to the rotation periods in various $B-V$-colour intervals. First,
we show that stars with vanishing magnetic activity, i.e. stars whose excess
flux index R$^{+}_{\rm{HK}}$ approaches zero, have a well-defined,
colour-dependent rotation period distribution; we also show that this rotation
period distribution applies to large samples of cool stars for which rotation
periods have recently become available. Second, we use empirical arguments to
equate this rotation period distribution with the global convective turnover
time, which is an approach that allows us to obtain clear relations between the
magnetic activity related excess flux index R$^{+}_{\rm{HK}}$, rotation
periods, and Rossby numbers. Third, we show that the activity versus Rossby
number relations are very similar in the different activity indicators. As a
consequence of our study, we emphasize that our Rossby number based on the
global convective turnover time approaches but does not exceed unity even for
entirely inactive stars. Furthermore, the rotation-activity relations might be
universal for different activity indicators once the proper scalings are used.
