The size evolution of platinum nanoparticles formed on a SiO2/Si(111) substrate as a function of the level of surface coverage with deposited clusters has been investigated. The anisotropic shapes of sub-nanometer-size nanoparticles are changed to isotropic on the amorphous substrate as their sizes increased. Using anomalous grazing incidence small-angle x-ray scattering (AGISAXS), the scattering from nanoparticles on the surface of a substrate is well separated from that of surface roughness and fluorescence. We show that AGISAXS is a very effective method to subtract the background and can provide unbiased information about particle sizes of less than 1 nm.