The dependence of the electrical conductivity on the oxygen partial pressure is calculated for the prototypical perovskite $\Ba\TiØ_3$ based on data obtained from first-principles calculations within density functional theory. The equilibrium point defect concentrations are obtained via a self-consistent determination of the electron chemical potential. This allows to derive charge carrier concentrations for a given temperature and chemical environment and eventually the electrial conductivity. The calculations are in excellent agreement with experimental data if an accidental acceptor dopant level of $10^{17}\,\cm^{-3}$ is assumed. It is shown that doubly charged oxygen vacancies are accountable for the high-temperature $n$-type conduction under oxygen-poor conditions. The high-temperature $p$-type conduction observed at large oxygen pressures is due to barium vacancies and titanium-oxygen di-vacancies under Ti and Ba-rich conditions, respectively. Finally, the connection between the present approach and the mass-action law approach to point defect thermodynamics is discussed. ; Comment: 9 pages, 5 figures