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Gaia  will obtain astrometry and spectrophotometry for essentially all sources in the sky down to a broad‐band magnitude limit of  G  = 20, an expected yield of 10 9  stars. Its main scientific objective is to reveal the formation and evolution of our Galaxy through chemodynamical analysis. In addition to inferring positions, parallaxes and proper motions from the astrometry, we must also infer the astrophysical parameters of the stars from the spectrophotometry, the blue photometer (BP)/red photometer (RP) spectrum. Here we investigate the performance of three different algorithms [Support Vector Machine (SVM),  ilium  and Aeneas] for estimating the effective temperature, line‐of‐sight interstellar extinction, metallicity and surface gravity of A–M stars over a wide range of these parameters and over the full magnitude range  Gaia  will observe ( G  = 6–20 mag). One of the algorithms, Aeneas, infers the posterior probability density function over all parameters, and can optionally take into account the parallax and the Hertzsprung–Russell diagram to improve the estimates. For all algorithms the accuracy of estimation depends on  G  and on the value of the parameters themselves, so a broad summary of performance is only approximate. For stars at  G  = 15 with less than 2 mag extinction, we expect to be able to estimate  T  eff  to within 1 per cent, log  g  to 0.1–0.2 dex and [Fe/H] (for FGKM stars) to 0.1–0.2 dex, just using the BP/RP spectrum (mean absolute error statistics are quoted). Performance degrades at larger extinctions, but not always by a large amount. Extinction can be estimated to an accuracy of 0.05–0.2 mag for stars across the full parameter range with a priori unknown extinction between 0 and 10 mag. Performance degrades at fainter magnitudes, but even at  G  = 19 we can estimate log  g  to better than 0.2 dex for all spectral types and    [   Fe   /  H  ]    to within 0.35 dex for FGKM stars, for extinctions below 1 mag.

The expected performance of stellar parametrization with Gaia spectrophotometry