The distinction between dimensions and units in physics is commonplace. But are dimensions a feature of reality? The most widely-held view is that they are no more than a tool for keeping track of the values of quantities under a change of units. This anti-realist position is supported by an argument from underdetermination: one can assign dimensions to quantities in many different ways, all of which are empirically equivalent. In contrast, I defend a form of dimensional realism, on which some (...) assignments of dimensions to quantities better describe reality than others. The argument I provide is a form of inference to the best explanation. In particular, the technique of dimensional analysis is explanatory, but it is only successful for certain systems of dimensions. Since these dimensional systems support scientific explanations, we have reason to believe that they are real. (shrink)