The radiation hazard for astronauts from galactic cosmic rays is a major obstacle in long duration human space explorations. Space radiation transport codes have been developed to calculate radiation environment on missions to the Moon, Mars or beyond. We have studied how uncertainties in fragmentation cross sections at different energies affect the accuracy of predictions from such radiation transport. We find that, in deep space, cross sections between 0.3 and 0.85 GeV/u usually have the largest effect on dose-equivalent behind shielding in solar minimum GCR environments, and cross sections between 0.85 and 1.2 GeV/u have the largest effect in solar maximum GCR environments. At the International Space Station, cross sections at higher energies have the largest effect due to the geomagnetic cutoff.