The thermally activated glide of screw dislocations in bcc crystals proceeds through the formation of kinks by pairs, a mechanism named after Peierls for his early work on dislocation theory. A method is proposed to compute the dislocation kink-pair formation enthalpy from density functional theory (DFT) calculations. This method consists of properly adjusting the parameters of a one-dimensional line tension model from atomistic calculations performed in small simulation cells. This model is applied to bcc iron to determine the kink-pair formation enthalpy at different applied stresses from DFT calculations.