The analysis, measurement, and management of species abundance is central to ecology and conservation biology, but it has proved difficult to find a single index that adequately reflects the commonness or rarity of species across a range of spatial scales. Here, a scale-independent measure of species abundance is developed, using presence-absence maps at varying spatial resolutions. By extrapolating such "scale-area" curves, species abundance can be estimated accurately even at scales finer than those used to parameterize the model, a task that had previously been deemed impossible in principle.