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CONTEXT: The unparalleled characteristics of Gaia photometry make it anexcellent choice to study stellar variability. AIMS: To measure the phot.dispersion in G+G_BP+G_RP of the 145 677 450 Gaia DR3 5-parameter sources withG <= 17 mag and G_BP-G_RP with -1.0 to 8.0 mag. To use that unbiased sample toanalyze stellar variability in the Milky Way, LMC, and SMC. METHODS: We convertfrom magnitude uncertainties to the observed phot. dispersions, calculate theinstrumental component as a function of apparent magnitude and color, and useit to transform the observed dispersions into the astrophysical ones. We givevariability indices in the three bands for the whole sample. We use thesubsample of Rimoldini et al. that includes light curves and variability typesto calibrate our results and establish their limitations. RESULTS: We useinformation from the MW, LMC, and SMC CAMDs to discuss variability across theHRD. WDs and sdBs are more variable than MS or RC stars but their variabilitydecreases for the former with age. The MS region in the Gaia CAMD has an s_Gdistribution peaks at low values (~1-2 mmag) and has a large tail dominated byEBs, RR Lyr stars, and YSOs. RC stars are characterized by little variability,with their s_G distribution peaking at 1 mmag or less. The stars in the PMSregion are highly variable, with a power law distribution in s_G with slope2.75 and a cutoff for values lower than 7 mmag. The luminous red stars regionof the Gaia CAMD has the highest variability, with its extreme dominated by AGBstars and with a power law in s_G with a slope of ~2.2 that extends from thereto a cutoff of 7 mmag. We show that our method can be used to search for LMCCepheids. We analyze four stellar clusters with O stars and detect a strongdifference in s_G between stars that are already in the MS and those that arestill in the PMS. [ABRIDGED BUT NOT TOO FAR]

Stellar variability in Gaia DR3. I. Three-band photometric dispersions for 145 million sources