The structure of samples of amorphous hydrogenated carbon, prepared from acetylene and propane precursors, containing 35 and 32 at. % hydrogen, respectively, was investigated by time-of-flight neutron diffraction in the range 0.2--50 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$ using the ISIS spallation source. The large dynamic range of the data ensures a real-space resolution sufficient to reveal directly the proportions of ${\mathit{sp}}^{2}$ and ${\mathit{sp}}^{3}$ hybridized carbon. The results show that, in these hard carbon materials, the carbon-atom sites are predominantly ${\mathit{sp}}^{2}$ bonded, and the carbon-carbon single bond:carbon-carbon double bond ratio is about 2.5:1. The detailed information on atomic correlations thus provided is used to discuss current structural models, and in particular the data are used to show that these models require significant modification.