The ICDD has implemented an option in Powder Diffraction File (PDF)-4 products to calculate time-of-flight (TOF) neutron powder diffraction patterns using atomic coordinates and structure information (the PDF-4+ 2016 has 271 499 entries that contain atomic coordinates and structure data). The calculated pattern data are used to populate PDF data cells and entries that contain d-spaces and neutron intensities, and are also available for calculated on-the-fly fully digitized patterns. To extend this on-the-fly capability, we include size and strain effects that affect the profile shapes. For specific application to TOF neutron diffraction full pattern analyses, a method was developed for calculating a background function. This method treats incoherent scattering and a zeroth order approximation to thermal diffuse scattering. The results are compared with experimental data from SRM 640C (Si), SRM 676 (Al2O3 corundum), SRM 660C (LaB6), and NAC (Na2La3Al2F14) instrument standards. Finally, a comparison of the calculated total patterns (Bragg scattering plus background) scattering contrast between Nd2Ni2InD7.52 and Nd2Ni2InH7.52 shows the value of neutron scattering simulation for planning experiments.