  We present empirical measurements of the radii of 116 stars that host
transiting planets. These radii are determined using only direct
observables-the bolometric flux at Earth, the effective temperature, and the
parallax provided by the Gaia first data release-and thus are virtually model
independent, extinction being the only free parameter. We also determine each
star's mass using our newly determined radius and the stellar density, itself a
virtually model independent quantity from previously published transit
analyses. These stellar radii and masses are in turn used to redetermine the
transiting planet radii and masses, again using only direct observables. The
median uncertainties on the stellar radii and masses are ~8% and ~30%,
respectively, and the resulting uncertainties on the planet radii and masses
are ~9% and ~22%, respectively. These accuracies are generally larger than
previously published model-dependent precisions of ~5% and ~6% on the planet
radii and masses, respectively, but the newly determined values are purely
empirical. We additionally report radii for 242 stars hosting radial-velocity
(non-transiting) planets, with median achieved accuracy of ~2%. Using our
empirical stellar masses we verify that the majority of putative "retired A
stars" in the sample are indeed more massive than ~1.2 Msun. Most importantly,
the bolometric fluxes and angular radii reported here for a total of 498 planet
host stars-with median accuracies of 1.7% and 1.8%, respectively-serve as a
fundamental dataset to permit the re-determination of transiting planet radii
and masses with the Gaia second data release to ~3% and ~5% accuracy, better
than currently published precisions, and determined in an entirely empirical
fashion.
