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The second Gaia data release (Gaia-DR2) contains, beyond the astrometry,three-band photometry for 1.38 billion sources. We have used these three broadbands to infer stellar effective temperatures, Teff, for all sources brighterthan G=17 mag with Teff in the range 3000-10 000 K (161 million sources). Usingin addition the parallaxes, we infer the line-of-sight extinction, A_G, and thereddening, E[BP-RP], for 88 million sources. Together with a bolometriccorrection we derive luminosity and radius for 77 million sources. Thesequantities as well as their estimated uncertainties are part of Gaia-DR2. Herewe describe the procedures by which these quantities were obtained, includingthe underlying assumptions, comparison with literature estimates, and thelimitations of our results. Typical accuracies are of order 324 K (Teff), 0.46mag (A_G), 0.23 mag (E[BP-RP]), 15% (luminosity), and 10% (radius). Being basedon only a small number of observable quantities and limited training data, ourresults are necessarily subject to some extreme assumptions that can lead tostrong systematics in some cases (not included in the aforementioned accuracyestimates). One aspect is the non-negativity contraint of our estimates, inparticular extinction. Yet in several regions of parameter space our resultsshow very good performance, for example for red clump stars and solaranalogues. Large uncertainties render the extinctions less useful at theindividual star level, but they show good performance for ensemble estimates.We identify regimes in which our parameters should and should not be used andwe define a "clean" sample. Despite the limitations, this is the largestcatalogue of uniformly-inferred stellar parameters to date. More precise anddetailed astrophysical parameters based on the full BP/RP spectrophotometry areplanned as part of the third Gaia data release.

Gaia Data Release 2: first stellar parameters from Apsis