This paper presents novel results on the electrical properties of amorphous carbon films prepared by ion-beam sputtering. The conductivity is found to be similar to that seen in evaporated carbon. Over the range approximately 40-300 K, it is well described by the variable range hopping equation with a hopping exponent of 1/2. This indicates that the density of localized states around the Fermi energy is parabolic. An analysis of the conductivity data in terms of variable range hopping in a Coulomb gap is quantitatively consistent, indicating that this could be the origin of the parabolic shape. A second possibility is that the parabolic gap is a remnant of the graphitic density of states, which is very small at the Fermi level. Field effect measurements on the carbon films were not able to distinguish between the two models, as both could be reconciled with the observed results, although in the case of the 'graphitic' gap a large density of surface traps is required to obtain a consistent interpretation.