Digitized outlines of sand grains from a dozen locations have been acquired using an optical microscope. A Fourier decomposition of the outline is calculated providing a spectral description of the grain’s shape. By averaging over several hundred grains, the normalized power spectrum of each sand sample is returned. The desert sands, beach sands, and marine sediments measured all exhibit the same inverse-power-law dependence on the harmonic number, n, varying as n−10/3 for 2⩽n⩽20. This “universal” spectrum provides the basis of a numerical technique for synthesizing the irregular outline of a sand grain: the outline is represented as a random pulse train in which identically shaped microasperities, with normally distributed amplitudes, are randomly superimposed on the perimeter of a circle. Carson’s theorem links the power spectrum of an individual microasperity to that of the real grains and constrains the synthetic outlines to have the identical statistical properties as the outlines of the measured samples. Visually, it is difficult to distinguish between the synthesized and real outlines. This numerical technique for synthesizing irregular outlines of grains has potential for investigating the random-packing of realistically rough particles through computer simulation. [Work supported by the Office of Naval Research.]