The results of intercept and profile counts are commonly interpreted as a suitable estimates of the mean grain size as represented e.g. by the grain density V. The term grain size is not explicitly defined even when some relation to grain volume and/or mean grain breadth (the mean Ferret diameter) is tacitly assumed. However, the intercept count L is directly related to the mean value of grain boundary area per unit volume SV and the profile count A is, under relatively general assumptions, directly related to the mean value of grain junctions per unit volume LV. Their relation to V can be generally written as V = c¢(A)3/2 = c²(L)3, but the coefficients c¢ and c² strongly depend on the structural characteristics like grain size dispersion, anisotropy etc. and their evaluation is far from being simple. Consequently, whereas the reliable estimates of SV and LV result from intercept and profile counts, the estimate of grain density based on them requires a careful consideration.