The initial concentration of monomeric amyloidogenic proteins is a crucial factor in the in vitro formation of amyloid fibrils. We use quantitative atomic force microscopy to study the effect of the initial concentration of human alpha-synuclein on the mean length of mature alpha-synuclein fibrils, which are associated with Parkinson's disease. We determine that the critical initial concentration, below which low-molecular-weight species dominate and above which fibrils are the dominant species, lies at approximately 15 muM, in good agreement with earlier measurements using biochemical methods. In the concentration regime where fibrils dominate, we find that their mean length increases with initial concentration. These results correspond well to the qualitative predictions of a recent statistical-mechanical model of amyloid fibril formation. In addition, good quantitative agreement of the statistical-mechanical model with the measured mean fibril length as a function of initial protein concentration, as well as with the fibril length distributions for several protein concentrations, is found for reasonable values of the relevant model parameters. The comparison between theory and experiment yields, for the first time to our knowledge, an estimate of the magnitude of the free energies associated with the intermolecular interactions that govern alpha-synuclein fibril formation.