The influence of disorder and stoichiometry-breaking point defects on the structural and magnetic properties of Sr2FeMoO6 have been investigated with the help of electronic structure calculations within the spin-polarized GGA+U approach. Defining the chemical potentials of the constituent elements from constitutional defects, we calculate the energetics of the possible point defects in nonstoichiometric Sr2FeMoO6 and find transition-metal-ion antisites and oxygen vacancies to be dominant. In nonstoichiometric Sr2Fe1+xMo1−xO6 with −0.75 ≤ x ≤ 0.25, both FeMo antisites (for Fe-rich samples or x > 0) and MoFe antisites (for Mo-rich samples or x < 0) lead to a systematic decrease in saturation magnetization. Only MoFe antisites destroy the half-metallic character of the electronic structure, since their t2g band crosses the Fermi level for x ≤ −0.125. This leads to a decrease of spin polarization from 100% for x ≥ −0.125 to 0 at x ≈ −0.75. Oxygen vacancies also reduce the saturation magnetization, but the half-metallic character and, hence, 100% spin polarization is retained. The optimized unit-cell lattice parameter remains within a relatively narrow range (7.96 Å for x = +0.25 to 8.00 Å for x = −0.75), despite large changes in composition. In stoichiometric Sr2FeMoO6, the saturation magnetization decreases linearly as the Fe/Mo antisite disorder increases, and the half metallicity is lost, because of the t2g states on both MoFe and FeMo. The spin polarization remains ∼100% only for very small amounts of disorder. The calculated disorder formation energies suggest that short-range ordering is favorable in Sr2FeMoO6. The calculated results are in excellent quantitative agreement with experimental values, where available.