Probability density functions (pdfs) are determined from newstellar parameters for the distance moduli of stars for which the RAdial Velocity Experiment (RAVE) has obtained spectra with S/N ≥ 10. Single-Gaussian fits to the pdf in distance modulus suffice for roughly half the stars, with most of the other half having satisfactory two-Gaussian representations. As expected, early-type stars rarely require more than one Gaussian. The expectation value of distance is larger than the distance implied by the expectation of distance modulus; the latter is itself larger than the distance implied by the expectation value of the parallax. Our parallaxes of Hipparcos stars agree well with the values measured by Hipparcos, so the expectation of parallax is the most reliable distance indicator. The latter are improved by taking extinction into account. The effective temperature-absolute magnitude diagram of our stars is significantly improved when these pdfs are used to make the diagram. We use the method of kinematic corrections devised by Schönrich, Binney and Asplund to check for systematic errors for general stars and confirm that the most reliable distance indicator is the expectation of parallax. For cool dwarfs and low-gravity giants, 〈 π{variant} 〉 tends to be larger than the true distance by up to 30 per cent. The most satisfactory distances are for dwarfs hotter than 5500 K. We compare our distances to stars in 13 open clusters with cluster distances from the literature and find excellent agreement for the dwarfs and indications that we are overestimating distances to giants, especially in young clusters. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. ; link_to_subscribed_fulltext