  There is a large literature on the asymptotic distribution of numbers free of
large prime factors, so-called $\textit{smooth}$ or $\textit{friable}$ numbers.
But there is very little known about this distribution that is numerically
explicit. In this paper we follow the general plan for the saddle point
argument of Hildebrand and Tenenbaum, giving explicit and fairly tight
intervals in which the true count lies. We give two numerical examples of our
method, and with the larger one, our interval is so tight we can exclude the
famous Dickman-de Bruijn asymptotic estimate as too small and the
Hildebrand-Tenenbaum main term as too large.
