High-resolution spectroscopy is the most accurate tool for measuring the properties of the solar corona. However, interpreting measured line intensities and line profiles emitted by the optically thin solar corona is complicated by line-of-sight (LOS) integration, which leads to measuring weighted averages of the plasma properties along the LOS. LOS integration effects can be removed by combining CHIANTI spectral emissivities with a 3D global model of the solar corona to calculate the contribution of all structures along the LOS to the measured intensities. In this paper, we describe SPECTRUM, a postprocessing tool that can calculate the emission from the optically thin solar corona by combining 3D magnetohydrodynamic (MHD) space plasma simulation results with the CHIANTI database. Doppler-shifted, nonthermal line broadening due to low-frequency Alfvén waves and anisotropic proton and isotropic electron temperatures can be individually taken into account during calculations. Synthetic spectral calculations can then be used for model validation, for interpretation of solar observations, and for forward modeling purposes. SPECTRUM is implemented within the Space Weather Modeling Framework (SWMF) and is therefore publicly available. In this paper, we describe the SPECTRUM module and show its applications by comparing synthetic spectra using simulation data by the 3D MHD Alfvén Wave Solar Model with observations done by the Hinode/Extreme-ultraviolet Imaging Spectrometer during Carrington rotations 2063 and 2082.