Supernova light curves are dominated at early time, hours to days, by photons escaping from the expanding shock heated envelope. We provide a simple analytic description of the time dependent luminosity, L, and color temperature, Tcol, for explosions of red supergiants (with convective polytropic envelopes), valid up to H recombination (T ≈ 0.7 eV). The analytic description interpolates between existing expressions valid at different (planar then spherical) stages of the expansion, and is calibrated against numerical hydrodynamic diffusion calculations for a wide range of progenitor parameters (mass, radius, core/envelope mass and radius ratios, metalicity), and explosion energies. The numerically derived L and Tcol are described by the analytic expressions with $10{{\%}}$ and $5{{\%}}$ accuracy respectively. Tcol is inferred from the hydrodynamic profiles using frequency independent opacity, based on tables we constructed for this purpose (and will be made publicly available) including bound-bound and bound-free contributions. In an accompanying paper (Paper II) we show, using a large set of multi-group photon diffusion calculations, that the spectral energy distribution is well described by a Planck spectrum with T = Tcol, except at UV frequencies, where the flux can be significantly suppressed due to strong line absorption. We defer the full discussion of the multi-group results to paper II, but provide here for completeness an analytic description also of the UV suppression. Our analytic results are a useful tool for inferring progenitor properties, explosion velocity, and also relative extinction based on early multi-band shock cooling observations of supernovae.