The radiation hazard for astronauts from galactic cosmic rays (GCR) is a major obstacle to long-duration human space exploration. Space radiation transport codes have been developed to calculate the radiation environment on missions to the Moon, Mars, and beyond. We have studied how uncertainties in fragmentation cross sections at different energies affect the accuracy of predictions from such radiation transport calculations. We find that, in deep space, cross sections at energies between 0.3 and 0.85 GeV/nucleon 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.