In scanning electron microscopy and low voltage point-projection microscopy there is considerable interest in estimating beam damage which can be related to the energy deposited in the specimen. We derive an expression for the energy deposition using the electron transport equation and give results for beam energies of 1-10 kV incident on 100 and 200 nm carbon films. The elastic scattering was modeled using a Rutherford cross section and the inelastic scattering cross section was derived from the Bethe stopping power equation. For the 100-nm-thick amorphous carbon film 90% of the incident beam energy is deposited in the sample at 2 keV, but at 6 keV only 20% of the energy is deposited. The 200 nm sample exhibited a similar curve with 20% deposition occurring at 9 kV. Our calculations show the same variation with beam energy as reported experimental results.