AbstractIntercept length distribution curves were calculated or determined graphically for a variety of polygons and shapes as an initial step in ascertaining the nature of intercept distributions for statistical grain sections, an intermediate goal being to provide a method of calculating section diameters from the more easily measured intercept distributions determined by lineal analysis, but with the ultimate aim of determining the spatial distribution. The following shapes were selected: an ellipse, an equilateral and an irregular triangle, a square, a 60°rhombus, a rectangle, a pentagon, a hexagon, an irregular seven sided polygon, and an irregular five sided polygon having convex sides. If the intercept length is designated as q and the distribution function as f(q), it is concluded that f(q) of a statistical grain section would have the following characteristics: f(q) finite at q=0, df(q)/dq≠0 at low values of q, f(q) a maximum at q