The atomistic study of kink pairs on screw dislocations in body-centered cubic (bcc) metals is challenging because interatomic potentials in bcc metals still lack accuracy and kink pairs require too many atoms to be modeled by first principles. Here, we circumvent this difficulty using a one-dimensional line tension model whose parameters, namely the line tension and Peierls barrier, are reachable to density functional theory calculations. The model parameterized in V, Nb, Ta, Mo, W, and Fe, is used to study the kink-pair activation enthalpy and spatial extension. Interestingly, we find that the atomistic line tension is more than twice the usual elastic estimates. The calculations also show interesting group tendencies with the line tension and kink-pair width larger in group V than in group VI elements. Finally, the present kink-pair activation energies are shown to compare qualitatively with experimental data and potential origins of quantitative discrepancies are discussed.