Single-event upsets (SEUs) affecting the configuration memory of a 28-nm field-programmable gate array (FPGA) have been studied through experiments and Monte Carlo modeling. This FPGA will be used in the front-end electronics of the electromagnetic calorimeter in PANDA (Antiproton Annihilation at Darmstadt), an upcoming hadron-physics experiment. Results from proton and neutron irradiations of the FPGA are presented and shown to be in agreement with previous experimental results. To estimate the mean time between SEUs during operation of PANDA, a Geant4-based Monte Carlo model of the phenomenon has been used. This model describes the energy deposition by particles in a silicon volume, the subsequent drift and diffusion of charges in the FPGA memory cell, and the eventual collection of charges in the sensitive regions of the cell. The values of the two free parameters of the model, the sensitive volume side $d = 87$ nm and the critical charge $Q_{\text {crit}} = 0.23$ fC, were determined by fitting the model to the experimental data. The results of the model agree well with both the proton and neutron data and are also shown to correctly predict the cross sections for upsets induced by other particles. The model-predicted energy dependence of the cross section for neutron-induced upsets has been used to estimate the rate of SEUs during initial operation of PANDA. At a luminosity of $1\cdot 10<^>{31}$ cm$<^>{-2}\,\,\text{s}<^>{-1}$ , the predicted mean time between upsets (MTBU) is between 120 and 170 h per FPGA, depending on the beam momentum.