Aims. We use Gaia Data Release 2 (DR2) to place 252 Herbig Ae/Be stars in the Hertzsprung–Russell diagram and investigate their characteristics and properties. Methods. For all known Herbig Ae/Be stars with parallaxes in Gaia DR2, we collected their atmospheric parameters and photometric and extinction values from the literature. To these data we added near-infrared and mid-infrared photometry, and collected Hα emission line properties such as equivalent widths and line profiles, and their binarity status. In addition, we developed a photometric variability indicator from Gaia’s DR2 information. Results. We provide masses, ages, luminosities, distances, photometric variabilities and IR excesses homogeneously derived for the most complete sample of Herbig Ae/Be stars to date. We find that high-mass stars have a much smaller IR excess and have much lower optical variabilities compared to lower-mass stars, with the break at around 7 M_⊙. Hα emission is generally correlated with IR excess, with the correlation being stronger for IR emission at wavelengths tracing the hot dust closest to the star. The variability indicator as developed by us shows that ∼25% of all Herbig Ae/Be stars are strongly variable. We observe that the strongly variable objects display doubly peaked Hα line profiles, indicating an edge-on disk. Conclusions. The fraction of strongly variable Herbig Ae stars is close to that found for A-type UX Ori stars. It had been suggested that this variability is in most cases due to asymmetric dusty disk structures seen edge-on. The observation here is in strong support of this hypothesis. Finally, the difference in dust properties occurs at 7 M_⊙, while various properties traced at UV/optical wavelengths differ at a lower mass, 3 M_⊙. The latter has been linked to different accretion mechanisms at work, whereas the differing IR properties and photometric variabilities are related to different or differently acting (dust-)disk-dispersal mechanisms.