The magnetic chemically peculiar (mCP) stars of the upper main sequence exhibit strong, globally organized magnetic fields that are inclined to the rotational axis and facilitate the development of surface abundance inhomogeneities resulting in photometric and spectroscopic variability. Therefore, mCP stars are perfectly suited for a direct measurement of the rotational period without the need for any additional calibrations. We have investigated the rotational properties of mCP stars based on an unprecedentedly large sample consisting of more than 500 objects with known rotational periods. Using precise parallaxes from the Hipparcos and Gaia satellite missions, well-established photometric calibrations and state-of-the-art evolutionary models, we have determined the location of our sample stars in the Hertzsprung-Russell diagram and derived astrophysical parameters such as stellar masses, effective temperature, radii, inclinations and critical rotational velocities. We have confirmed the conservation of angular momentum during the main sequence evolution; no signs of additional magnetic braking were found. The inclination angles of the rotational axes are randomly distributed, although an apparent excess of fast rotators with comparable inclination angles has been observed. We have found a rotation rate of v/v_crit_>=0.5 for several stars, whose characteristics cannot be explained by current models. For the first time, we have derived the relationship between mass and rotation rate of mCP stars, and provide an analysis that links mass and rotation with magnetic field strength. Our sample is unique and offers crucial input for forthcoming evolutionary models that include the effects of magnetic fields for upper main sequence stars.