Stellar distances constitute a foundational pillar of astrophysics. The publication of 1.47 billion stellar parallaxes from Gaia is a major contribution to this. Here is a catalogue of geometric distances for 1.47 billion stars and photogeometric distances for 92% of these. These estimates, and their uncertainties, can also be used as estimates of the distance modulus. Geometric distances use only the EDR3 parallaxes. Photogeometric distances additionally use the G magnitude and BP-RP colour from EDR3. Both types of estimate involve directiondependent priors constructed from a sophisticated model of the 3D distribution, colours, and magnitudes of stars in the Galaxy as seen by Gaia, i.e. accommodating both interstellar extinction and a Gaia selection function. Tests on mock data, but moreover validation against independent estimates and open clusters, suggest our estimates are reliable out to several kpc. For faint or more distant stars the prior will often dominate the estimates.