With the ever growing number of detected and confirmed exoplanets, the probability to find a planet that looks like the Earth increases continuously. While it is clear that being in the habitable zone does not imply being habitable, a systematic study of the evolution of the habitable zone is required to account for its dependence upon stellar parameters. In this study, we aim to provide the community with the dependence of the habitable zone upon the stellar mass, age, metallicity, and rotation. We use stellar evolution models computed with the STAREVOL code to study the evolution of the habitable zone. Mass and metallicity are the stellar parameters that have the most dramatic effects on the habitable zone limits. The evolution of the habitable zone limits is also linked to the evolution of the stellar activity (through the Rossby number) that depends on the considered stellar mass and rotation. Using observed trends of stellar magnetic field strength we also constrain the planetary magnetic field (at the zero order) required for a sufficient magnetospheric protection during the whole stellar evolution. We explicit for the first time the systematic dependence of planet habitability on stellar metallicity and rotation along the full evolution of low- and intermediate-mass stars. These results can be used as physical inputs for a first order estimation of exoplanetary habitability.