We have used different computational methods, including B3LYP, CCSD(T)-F12 and CBS-QB3, to study and compare the addition–elimination reaction of the nitrate radical NO₃ with four sulfur-containing species relevant to atmospheric chemistry: hydrogen sulfide (H₂S), dimethyl sulfide [(CH₃)₂S], dimethyl sulfoxide [(CH3)₂SO] and sulfur dioxide (SO₂). We find that the reaction with (CH₃)₂SO to give NO₂ + (CH₃)₂SO₂ has a very low barrier, and is likely to be the dominant oxidation mechanism for (CH₃)₂SO in the atmosphere. In agreement with previous experimental data and computational results, we find that the reaction with H₂S and SO₂ is very slow, and the reaction with (CH₃)₂S is not competitive with the hydrogen abstraction route. The differences in reaction energetics and rates between the four species are explained in terms of stabilizing interactions in the transition states and differences in sulfur–oxygen bond strengths.