Sand grains occurr in different shapes and sizes according to mineral composition, age, transport mechanism and distance traveled. Old sands usually have a round shape due to repeated wheatering and action of external factors. If they are exposed to strong wind or tidal action, the roundness of the grains are more accentuated as for the more “static” sands. On opposite, younger sands produced artificially by crushing sandstone tend to be more irregular in shape, with “sharp” edges. Along a river, bigger (and heavier) particles are deposided upstream and the lighter grains are being carried away a longer distance and thus more prone to accentuated roundness.

Two geometrical parameters are used to describe the shape of sand grains, namely roundness and sfericity. Roundness is the measure describing the sharpness of a grain’s corners and edges, regardless of shape. A rather exact description of particle roundness has been proposed in 1932 by a scientist called Wadell as “the ratio of the average radius of curvature of the several edges or corners of the particle to the radius of curvature of the maximum inscribed sphere”. A perfect rounded particle would have the roundness = 1, all the others being included in different roundness classes (see also image below): well rounded (roundness value between 0.60 – 1.00), rounded (0.40 – 0.60), subrounded (0.25 – 0.40), subangular (0.15 – 0.25), angular (0.00 – 0.15), and very angular (class reserved for grains with extremely sharp edges).

Modified after Powers, M . C., 1953, Journal of Sedimentary Petrology, v. 23, p. 118

Sphericity is a measure of the degree to which the shape of a particle approaches that of a sphere. A perfect spherical grain would have the sfericity factor = 1 but this is rather uncommon in nature as most sand grains have sphericity numbers around 0.7 (in the image above, grains on the top line would have high sphericity values and those at the bottom low values).

Although elaborated methods have been developed for exact measuring the both parameters (e.g. by surface area measurement using laser scanner or using shape analysis sofware like ArcInfo), in practice more easier visual methods are used, such as Krumbein roundness chart and Riley sphericity index. For a better exemplification I inserted two images depicting quartz sands with different grain roundness and sphericity(left: subangular grains, right: rounded grains):

More info on roundness and sphericity:

• Krumbein, W. C. and L. L. Sloss (1951) Stratigraphy and Sedimentation. 2^nd. Ed. W. H. Freeman and Company. London
• Vepraskas, M. J. and Cassel, D. K. (1987) Sphericity and Roundness of Sand in Coastal Soils and Relationships with Soil Physical Properties. Soil Sci. Soc. Am. J. 51:1108-1112