An objective procedure is described for quantifying the shape of two-dimensional closed curves from projections or sections of particles, e.g., sand grains. The curves are plotted in polar coordinates r and θ, and a harmonic analysis is made of the function r(θ) by numerical analysis of measurements at equally spaced sample points along the curves. Quantities corresponding to the conventional properties of sphericity and roundness are derived from the Fourier coefficients. Three different measures of roundness are proposed and shown to correlate with visually estimated roundness classes, though also depending to some extent on sphericity. An attempt is described to study the interaction between these two properties by analysis of synthetically rounded plastic particles.