The shapes of flat pebbles may be characterized in terms of the statistical distribution of curvatures measured along their contours. We illustrate this method for clay pebbles eroded in a controlled laboratory apparatus, and also for naturally occurring rip-up clasts formed and eroded in the Mont St.-Michel bay. We find that the curvature distribution allows finer discrimination than traditional measures of aspect ratios. Furthermore, it connects to the microscopic action of erosion processes that are typically faster at protruding regions of high curvature. We discuss in detail how the curvature may be reliably deduced from digital photographs.