Segregation energies of oxygen vacancies and protons near three symmetric tilt grain boundaries in BaZrO3 are determined using density functional theory. Two of the grain boundaries have the [110] direction as tilt axis with a (111) or (112) plane as grain boundary plane, while the third has the [001] direction as tilt axis and a (210) plane as grain boundary plane. Both defects are found to segregate to all three grain boundaries, with vacancy segregation energies of −0.5 eV and −1.5 eV and proton segregation energies of about −0.8 eV. The effects of the calculated segregation energies on defect concentrations and electrostatic potential in the grain boundary region are investigated using a thermodynamic space charge model. An increased concentration of defects is seen in all grain boundaries, giving electrostatic potential barriers around 0.6 V at 400-600 K. Protons are found to give important contributions to the space charge in all three grain boundaries.