The differential flux J(E) observed in space radiations can be related to the characteristics of the particle momentum distribution functions. In fitting flux spectra by a sum of Maxwellians or by power laws, the slope of the differential flux is associated with the characteristic energy of the distributions and the normalization constant is proportional to the density. The goal of this work is to obtain a density-energy description of the radiation belts by using the kinetic approach. Starting from the proton spectra of the radiation belt models AP-8 MIN and AP-8 MAX, we show that the best fits are given by a power law at 1.8L < 4 while a sum of two Maxwellians give best fits at large radial distances. Assuming the correspondence between the momentum distributions and the observed spectra, we determine the variations of number density and energy with the radial distance, with the latitude and during minimum and maximum solar activity. This analysis provides information on the origin and mechanisms influencing the radiation populations.