The basic unified model of active galactic nuclei (AGNs) invokes an anisotropic obscuring structure, usually referred to as a torus, to explain AGN obscuration as an angle-dependent effect. We present a new grid of X-ray spectral templates based on radiative transfer calculations in neutral gas in an approximately toroidal geometry, appropriate for CCD-resolution X-ray spectra (FWHM ≥ 130 eV). Fitting the templates to broadband X-ray spectra of AGNs provides constraints on two important geometrical parameters of the gas distribution around the supermassive black hole: the average column density and the covering factor. Compared to the currently available spectral templates, our model is more flexible, and capable of providing constraints on the main torus parameters in a wider range of AGNs. We demonstrate the application of this model using hard X-ray spectra from NuSTAR (3-79 keV) for four AGNs covering a variety of classifications: 3C 390.3, NGC 2110, IC 5063, and NGC 7582. This small set of examples was chosen to illustrate the range of possible torus configurations, from disk-like to sphere-like geometries with column densities below, as well as above, the Compton-thick threshold. This diversity of torus properties challenges the simple assumption of a standard geometrically and optically thick toroidal structure commonly invoked in the basic form of the unified model of AGNs. Finding broad consistency between our constraints and those from infrared modeling, we discuss how the approach from the X-ray band complements similar measurements of AGN structures at other wavelengths.