We present a comprehensive sample of all gamma-ray burst (GRB) afterglows with known distances, and we derive their conical opening angles based on observed broadband breaks in their light curves. Within the framework of this conical jet model, we correct for the geometry and we find that the gamma-ray energy release is narrowly clustered around 5×1050 ergs. We draw three conclusions. First, the central engines of GRBs release energies that are comparable to ordinary supernovae. Second, the broad distribution in fluence and luminosity for GRBs is largely the result of a wide variation of opening angles. Third, only a small fraction of GRBs are visible to a given observer, and the true GRB rate is several hundred times larger than the observed rate.