The similarity of Reynolds and Mach number for model and full scale fan cannot be retained for the dimensioning of large industrial fans. Scaling is supposed to compensate these differences in efficiency determination. The present paper indicates the influence of compressibility, e. g. the Mach number on efficiency and efficiency scaling of fans. The research is focused on experimental investigations and the use of common scaling laws proposed by Ackeret [1] and Pelz/Stonjek [2]. The investigations were done at the laboratories of the Chair of Fluid Systems at the Technische Universität Darmstadt, Germany. A centrifugal fan with the specific speed σ = 0.114 was chosen because of its high pressure rise and high operating Mach number. As expected, the results show an increase in maximum efficiency by increasing Reynolds and Mach number up to ܽMa < 0.3. If the Reynolds and Mach number are increased further, the maximum efficiency stagnates and decreases for Mach numbers above ܽMa > 0.4. Both mentioned scaling laws consider the variation of Reynolds number, but none of them consider the effects of a change in Mach number. But a change in Mach number affects the friction losses, Carnot losses and incidence losses, which are discussed for the present fan as well.