Models based on the amorphous track structure approximation have been successful in predicting the biological effects of heavy charged particles. Development of such models remains an active area of research that includes applications to hadrontherapy. In such models, the radial distribution of the dose deposited by delta electrons and directly by the particle is the main characteristic of track structure. We calculated these distributions with Geant4-DNA Monte Carlo code for protons in the energy range from 10 to 100 MeV. These results were approximated by a simple formula that combines the well-known inverse square distance dependence with two factors that eliminate the divergence of the radial dose integral at both small and large distances. A clear physical interpretation is given to the asymptotic behaviour of the radial dose distribution resulting from these two factors. The proposed formula agrees with the Monte Carlo data within 10% for radial distances of up to 10 μm, which corresponds to a dose range covering over eight orders of magnitude. Differences between our results and those of previously published analytical models are discussed.