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We present empirical measurements of the radii of 116 stars that hosttransiting planets. These radii are determined using only directobservables-the bolometric flux at Earth, the effective temperature, and theparallax provided by the Gaia first data release-and thus are virtually modelindependent, extinction being the only free parameter. We also determine eachstar's mass using our newly determined radius and the stellar density, itself avirtually model independent quantity from previously published transitanalyses. These stellar radii and masses are in turn used to redetermine thetransiting planet radii and masses, again using only direct observables. Themedian uncertainties on the stellar radii and masses are ~8% and ~30%,respectively, and the resulting uncertainties on the planet radii and massesare ~9% and ~22%, respectively. These accuracies are generally larger thanpreviously published model-dependent precisions of ~5% and ~6% on the planetradii and masses, respectively, but the newly determined values are purelyempirical. We additionally report radii for 242 stars hosting radial-velocity(non-transiting) planets, with median achieved accuracy of ~2%. Using ourempirical stellar masses we verify that the majority of putative "retired Astars" 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 planethost stars-with median accuracies of 1.7% and 1.8%, respectively-serve as afundamental dataset to permit the re-determination of transiting planet radiiand masses with the Gaia second data release to ~3% and ~5% accuracy, betterthan currently published precisions, and determined in an entirely empiricalfashion.

Accurate, Empirical Radii and Masses of Planets and their Host Stars with Gaia Parallaxes