  We derive an analytic prediction for the star formation rate in environments
ranging from normal galactic disks to starbursts and ULIRGs in terms of the
observables of those systems. Our calculation is based on three premises: (1)
star formation occurs in virialized molecular clouds that are supersonically
turbulent; (2) the density distribution within these clouds is lognormal, as
expected for supersonic isothermal turbulence; (3) stars form in any sub-region
of a cloud that is so overdense that its gravitational potential energy exceeds
the energy in turbulent motions. We show that a theory based on this model is
consistent with simulations and with the observed star formation rate in the
Milky Way. We use our theory to derive the Kennicutt-Schmidt Law from first
principles, and make other predictions that can be tested by future
observations. We also provide an algorithm for estimating the star formation
rate that is suitable for inclusion in numerical simulations.
