Density functional theory (DFT) methods, as implemented in the Vasp code, are used to calculate the inelastic neutron scattering (INS) spectrum of urea, which has been measured on the Tosca spectrometer at ISIS, UK and the NERA-PR spectrometer at Dubna, Russia. Urea presents an extended network of bifurcated hydrogen bonds resulting in significant dispersion of the vibrational excitations, both for external and internal modes. The small mass of the molecule also results in intense multiphonon contributions to the spectral profile. Recent, successful applications of DFT in molecular spectroscopy are extended here using the Phonon code to include dispersion and multiphonon contributions to the INS spectrum. Thus the whole spectral profile is calculated with only the crystal structure as input. The accuracy of the calculated normal modes is demonstrated for protonated and deuterated urea.