Slow drift is a large, low-frequency motion of a floating platform caused by nonlinear hydrodynamic forces. Although slow drift is a well-known phenomenon for ships and other floating structures, new platforms for floating wind turbines are significantly smaller in scale, and it is yet to be established how important slow drift is for them. In this paper we derive an approximate expression for the scaling of the slow drift motion with platform size, mooring characteristics and wave conditions. This suggests that slow drift may be less important for floating wind turbines than other, larger, floating structures. The accuracy of the approximations is discussed; in the one case where detailed data is available, the approximate result is found to be conservative by a factor of up to 40.