We present a novel decomposition of non-negative functional count data, which we call NNFPCA (non-negative functional principal components analysis), that draws on ideas from non-negative matrix factorization. Our decomposition enables the study of patterns of variation across subjects in a highly interpretable manner. FPCs are estimated directly on the data scale, are local and represent parts that are transparently combined together via addition. This contrasts with generalized FPC approaches, which estimate FPCs on a latent scale, where decompositions of observations reflect highly complex patterns of cancellation and multiplication of FPCs that often vary across their entire domain. We apply our decomposition method to a dataset comprising observations of physical activity for elderly healthy Americans.