The magnetic activity of late-type stars is correlated with their rotation rates. Up to a certain limit, stars with smaller Rossby numbers, defined as the rotation period divided by the convective turnover time, have higher activity. A more detailed look at this rotation-activity relation reveals that, rather than being a simple power-law relation, the activity scaling has a shallower slope for the low-Rossby stars than for the high-Rossby ones. We find that, for the chromospheric Ca II H&K activity, this scaling relation is well modeled by a broken two-piece power law. Furthermore, the knee point of the relation coincides with the axisymmetry to nonaxisymmetry transition seen in both the spot activity and surface magnetic field configuration of active stars. We interpret this knee point as a dynamo transition between dominating axi- and nonaxisymmetric dynamo regimes with a different dependence on rotation and discuss this hypothesis in the light of current numerical dynamo models.