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Stellar distances constitute a foundational pillar of astrophysics. Thepublication of 1.47 billion stellar parallaxes from Gaia is a majorcontribution to this. Yet despite Gaia's precision, the majority of these starsare so distant or faint that their fractional parallax uncertainties are large,thereby precluding a simple inversion of parallax to provide a distance. Herewe take a probabilistic approach to estimating stellar distances that uses aprior constructed from a three-dimensional model of our Galaxy. This modelincludes interstellar extinction and Gaia's variable magnitude limit. We infertwo types of distance. The first, geometric, uses the parallax together with adirection-dependent prior on distance. The second, photogeometric, additionallyuses the colour and apparent magnitude of a star, by exploiting the fact thatstars of a given colour have a restricted range of probable absolute magnitudes(plus extinction). Tests on simulated data and external validations show thatthe photogeometric estimates generally have higher accuracy and precision forstars with poor parallaxes. We provide a catalogue of 1.47 billion geometricand 1.35 billion photogeometric distances together with asymmetric uncertaintymeasures. Our estimates are quantiles of a posterior probability distribution,so they transform invariably and can therefore also be used directly in thedistance modulus (5log10(r)-5). The catalogue may be downloaded or queriedusing ADQL at various sites (seehttp://www.mpia.de/homes/calj/gedr3_distances.html) where it can also becross-matched with the Gaia catalogue.

Estimating distances from parallaxes. V: Geometric and photogeometric distances to 1.47 billion stars in Gaia Early Data Release 3