Measurements are presented of the t-channel single-top-quark production cross section in proton-proton collisions at= 8 TeV. The results are based on a data sample corresponding to an integrated luminosity of 19.7 fb− 1 recorded with the CMS detector at the LHC. The cross section is measured inclusively, as well as separately for top (t) and antitop, in final states with a muon or an electron. The measured inclusive t-channel cross section is σしぐま t-ch.= 83. 6±2. 3 (stat.)±7. 4 (syst.) pb. The single t and cross sections are measured to be σしぐま t-ch.(t)= 53. 8±1. 5 (stat.)±4. 4 (syst.) pb and σしぐま t-ch.= 27. 6±1. 3 (stat.)±3. 7 (syst.) pb, respectively. The measured ratio of cross sections is R t-ch.= σしぐま t-ch.(t)/σしぐま t-ch.= 1. 95±0. 10 (stat.)±0. 19 (syst.), in agreement with the standard model prediction. The modulus of the Cabibbo-Kobayashi-Maskawa matrix element V tb is extracted and, in combination with a previous CMS result at= 7 TeV, a value| V tb|= 0. 998±0. 038 (exp.)±0. 016 (theo.) is obtained.