The results of relativistic photocurrent calculations, based on the one-step model of photoemission, used here to simulate inverse photoemission spectroscopy (IPES) experiments from the W(001) and W(110) surfaces are presented. The isochromat IPES spectra, for photon energies ranging between 15 and 30 eV, were recorded for electrons incident normal to the (001) and (110) crystal surfaces, corresponding to transitions in the Gamma H and Gamma N directions of the three-dimensional Brillouin zone respectively. This combined theoretical and experimental study is used to investigate the electronic structure, in particular the bulk electronic structure, of these systems. The calculated spectra are found to be in good overall agreement with the corresponding experimental results. The origins of the remaining discrepancies between theory and experiment are discussed.