Though widely observed to be emanating from a variety of astrophysical sources, the underlying physical mechanism behind the formation of galactic and extragalactic outflows is still enshrouded in a veil of mystery. In addition. it has not been possible to calculate accurately the amount of matter expelled in these events. In this article we present a non-self-similar analytical model, which, for the first time, we believe is able to explain the outflow formation phenomenon as well as compute the mass outflow rate by simultaneously solving the equations governing the exact transonic accretion and outflow, Our model predicts the dependence of this rate on various flow parameters as well as indicates the exact location from where the outflows are launched.