A convenient property of energetic heavy charged particles in passing through matter is that the primaries and their secondary particles remain relatively confined to the primary beam axis. As a consequence, the particle beam in matter is not strongly affected by near boundaries and the problem of calculating dose in a complicated geometric object is greatly simplified. Furthermore, the small beam width is a useful expansion parameter to develop a series that converges rapidly for most practical dose calculations. The final result relates dose at any point in an arbitrary convex region to an integral over the fluence-to-dose conversion factors for normal incidence on a semi-infinite slab. A representation of these fluence-to-dose conversion factors and all the necessary information required to calculate dose in arbitrary convex regions of tissue for proton energies below 1 GeV are found in terms of two energy-dependent parameters and known functions.