Over the last forty years much progress has been made in the investigation of the scale of a uniform space. In particular, Bushaw, Kent, Ramsey and Richardson published several articles concerning the scale of a uniform space. The aim of this dissertation is to begin a similar investigation into the scale of a quasi-uniform space. It starts off with a summary of results obtained for the scale of a uniform space, which, has been investigated in the past. We conclude by commencing an investigation into the scale of a quasi-uniform space. Here several results obtained for the scale of a uniform space are generalized, and some original results for the scale of a quasi-uniform space are presented. Includes bibliographical references (pages 76-79).