Alongside volume fraction, VV, and area per unit of volume, SV, the integral interface curvature per unit of volume, MV, or the average interface curvature, H, are important microstructural descriptors. For grain growth, the grain boundary curvature is of special importance because, in addition to its geometrical significance, it is also the driving force for boundary migration. Notwithstanding its importance, curvature has been seldom measured and utilized in the analysis of polycrystals. Geometrical models were derived for the average curvature of individual grains, of grain boundaries and of grain edges, as a function of the mean intercept length. These models show good agreement with curvature measurements in an Al-1mass%Mn alloy. Furthermore, this work shows how grain boundary curvature measurement can be applied to normal grain growth as well as to the effect of particles on grain boundary pinning.