The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider. The full Run 2 data sample recorded with the ATLAS detector in the years 2015–2018 is used, corresponding to an integrated luminosity of 140 fb−1. The absolute and normalised production cross-sections are measured differentially as a function of the transverse momentum and absolute rapidity of the top quark and top antiquark. In addition, the ratio of top quark to top antiquark production cross-sections is measured. The measured distributions are compared with next-to-leading-order quantum chromodynamics predictions obtained with different combinations of matrix-element generators, parton-shower programs and proton parton distribution functions, as well as to next-to-next-to-leading-order calculations. Overall, good agreement is observed between the measurements and the theoretical predictions. For most measured distributions, the sensitivity to differences between the predictions is limited by the systematic uncertainties in the measurement. The measured differential distributions are also interpreted in an effective field theory approach to constrain the Wilson-Coefficient CQq3,1 associated with a four-quark operator. The interpretation accounts for the effect of the selection efficiency, which is altered significantly by non-zero contributions from CQq3,1.