Making use of our extended version of ¨ O p i k ′ s convection theory, we have calculated magnetic cycle periods of the sun and late type stars by using Parker's dynamo theory, where we have included the non-linear effect. We presented a relationship between the computed cycle period and spectral type to analyze observed magnetic activities of the late type stars and long-term luminosity variations. It is found that (1) the stellar magentic-cycle period increases towards the later spectral type, (2) the rapid rotation facilitates the activity-related luminosity variation of stars later than about K5, (3) differential rotation plays a critical role in determining the magnetic activity-cycle period, and (4) the non-local effect should be taken into account in order to understand the observed long-term luminosity variations.