We present a method to establish, experimentally, the relation between the top-quark mass mMC t asimplemented in Monte Carlo generators and the Lagrangian mass parameter mt in a theoretically welldefinedrenormalization scheme. We propose a simultaneous fit of mMCt and an observable sensitive to mt,which does not rely on any prior assumptions about the relation between mt and mMCt . The measuredobservable is independent of mMCt and can be used subsequently for a determination of mt. The analysisstrategy is illustrated with examples for the extraction of mt from inclusive and differential cross sectionsfor hadroproduction of top quarks.