  Gamma-ray bursts (GRBs) are the most brilliant objects in the Universe but
efforts to estimate the total energy released in the explosion -- a crucial
physical quantity -- have been stymied by their unknown geometry: spheres or
cones. We report on a comprehensive analysis of GRB afterglows and derive their
conical opening angles. We find that the gamma-ray energy release, corrected
for geometry, is narrowly clustered around 5x10**50 erg. We draw three
conclusions. First, the central engines of GRBs release energies that are
comparable to ordinary supernovae, suggesting a connection. Second, the wide
variation in fluence and luminosity of GRBs is due entirely to a distribution
of opening angles. Third, only a small fraction of GRBs are visible to a given
observer and the true GRB rate is at least a factor of 500 times larger than
the observed rate.
