Activity caused by surface magnetism is a pervasive feature of cool late-type stars where a dynamo mechanism is supported in the outer convective envelopes of the stellar interiors. The detailed mechanism responsible for this dynamo is still debated but its basic ingredients include convective turbulence and non-uniformities in the stellar rotation profile 1 , although the role of the former divides opinions. Both the observed surface magnetic fields 2 and activity indicators from the chromosphere 3 to the transition region 4 and corona 5 are known to be closely connected with the stellar rotation rate. These relationships have been intensely studied in recent years, some works indicating that the activity should be related to the Rossby number 5, 6 , quantifying the stellar rotation in relation to the convective turnover time, while others claim that the tightest correlation can be achieved using the rotation period alone 7, 8 .Here we tackle this question by including evolved giant stars to the analysis of the rotationactivity relation. These stars rotate very slowly compared to the main sequence stars, but still show strikingly similar activity levels 9 . We show that by using the Rossby number, the two stellar populations fall together in the rotation-activity diagram, and follow the same activity scaling. This suggests that turbulence has a key role in driving stellar dynamos, and that there appears to be a universal turbulence-related dynamo mechanism explaining magnetic activity levels of both main sequence and evolved stars.