We present bolometric fluxes and angular diameters for over 1.6 million stars in the Tycho-2 catalog (I/259), determined using previously determined empirical color-temperature and color-flux relations. We vet these relations via full fits to the full broadband spectral energy distributions for a subset of benchmark stars and perform quality checks against the large set of stars for which spectroscopically determined parameters are available from LAMOST, RAVE, and/or APOGEE. We then estimate radii for the 355502 Tycho-2 stars in our sample whose Gaia DR1 (I/337) parallaxes are precise to ~<10%. For these stars, we achieve effective temperature, bolometric flux, and angular diameter uncertainties of the order of 1%-2% and radius uncertainties of order 8%, and we explore the effect that imposing spectroscopic effective temperature priors has on these uncertainties. These stellar parameters are shown to be reliable for stars with T_eff_~<7000 K. The over half a million bolometric fluxes and angular diameters presented here will serve as an immediate trove of empirical stellar radii with the Gaia second data release, at which point effective temperature uncertainties will dominate the radius uncertainties. Already, dwarf, subgiant, and giant populations are readily identifiable in our purely empirical luminosity-effective temperature (theoretical) Hertzsprung-Russell diagrams.