We investigate the influence of the spatial spreading effect in a proton arc with finite width on resulting primary ionization rates, using our three-dimensional (3-D) Monte Carlo ion transport model. By the direct impact from energetic protons and generated hydrogen atoms, ambient neutrals in the Earth's upper atmosphere can be ionized in charge exchange or ionization collisions. The model results show that the ionization rates (and particle fluxes) depend on all of the parameters we varied: incident proton arc dimensions, energy spectra, average energies, latitudinal energy flux distributions, and magnetic field dip angles. It is found that a correction factor, often introduced at an equilibrium altitude (~300 km) in one-dimensional (1-D) theoretical models, cannot completely account for the beam spreading effect for an incident proton arc of finite width. Below ~300 km, ionization rates in 1-D models are generally overestimated at high altitudes (above ~150 km) and underestimated at low altitudes (below ~150 km). The overestimation is caused by overlooking the difference between the spatial spreading for the particle fluxes and for the ionization rates. At low altitudes, the beam radius gets smaller, causing underestimation in the 1-D ionization rates. The results of our 3-D sensitivity study of various parameters can be applied in future studies of auroral and ring current proton precipitation into the upper atmosphere.