From an extensive calculation of static properties of a trapped Fermi superfluid at zero temperature using a density-functional formulation, we demonstrate a universal behavior of its observables, such as energy, chemical potential, radius, etc., over the crossover from the BCS limit to unitarity leading to scaling over many orders of magnitude in fermion number. This scaling allows us to predict the static properties of the system, with a large number (similar to 10(5)) of fermions, over the crossover with an error of 1%-2%, from the knowledge of those for a small number (similar to 10) of fermions.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)