Inherited quartz overgrowths represent remnants of cement adhering to a grain's surface from a previous sedimentary cycle and can be recognized in petrographic studies on the basis of textural criteria. Since these features occupy only a part of a grain's surface and are randomly positioned, when studied in two-dimensional sections the likelihood of their being transected and observed is significantly less than their whole-rock abundance. This has resulted is an underestimation of their importance as a provenance indicator. An experiment using an eccentric steronet was devised to analyze the relationship between size of a grain-coating cap and likelihood that it will be transected in a random cut. Since size of a coating cap is related to its projection angle measured from the sphere's center, a second experiment was devised to determine the relationship between projection angles and equivalent apparent projection angles seen when a cut does not pass through a sphere's center. It was found that the true projection angle equals the mode of apparent projection angles. Relationships determined in these two experiments enable calculation of the whole-rock proportion of grains with inherited overgrowths from petrographic data. The procedure was applied to samples of Upper Precambrian quartz arenites from the Uinta Mountain Group, the Grand Canyon Supergroup, and the Belt Supergroup, resulting in calculated whole-rock proportions of grains with inherited overgrowths that are, in general, twice the values observed in thin section. This procedure may also be useful in studies of sediment distribution, intrabasinal sediment maturation, lithostratigraphic correlation, and rates of grain surface abrasion.--Modified journal abstract.