Self-diffusion coefficients for liquid n-hexane measured by the n.m.r. spin–echo technique are reported at 223, 248, 273, 298 and 333 K at pressures up to 400 MPa. Owing to a marked non-linear volume dependence, the results could not be directly fitted to the rough hard-sphere model of diffusion, but reduced diffusion coefficients were fitted as a function of a reduced volume, expressed as the ratio of the molar volume to a ‘hard-core volume’. The temperature dependence of an equivalent hard-sphere diameter calculated from this hard-core volume was found to be adequately represented by an equation originally proposed by Protopapas, Andersen and Parlee for liquid metals: σ=σ0[1–B(T/Tm)½]. The constant B, 0.072, is of similar magnitude to that found to fit CH4 and C2H4 self-diffusion data, 0.069, and is consistent with diameters derived from the viscosity measurements of Brazier and Freeman. Between 273 and 333 K where the diffusion and viscosity results overlap, the group Dηt is constant, at a given temperature, with t= 0.97: consequently the Stokes–Einstein equation is not obeyed.