Measurements of the cross sections for the production of single top quarks and antiquarks in the t channel, and their ratio, are presented for proton-proton collisions at a center-of-mass energy of 13 TeV. The data set used was recorded in 2016 by the CMS detector at the LHC and corresponds to an integrated luminosity of 35.9 fb−1. Events with one muon or electron are selected, and different categories of jet and b jet multiplicity and multivariate discriminators are applied to separate the signal from the background. The cross sections for the t-channel production of single top quarks and antiquarks are measured to be 130±1(stat)±19(syst)pb and 77±1(stat)±12(syst)pb, respectively, and their ratio is 1.68±0.02(stat)±0.05(syst). The results are in agreement with the predictions from the standard model.