Measurements are presented of the t-channel single-top-quark production cross section in proton-proton collisions at $ \sqrt{s} $ = 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 $ \left(\overline{\mathrm{t}}\right) $ , in final states with a muon or an electron. The measured inclusive t-channel cross section is σ${t-ch.}$ = 83.6 ± 2.3 (stat.) ± 7.4 (syst.) pb. The single t and $ \overline{\mathrm{t}} $ cross sections are measured to be σ${t-ch.}$(t) = 53.8 ± 1.5 (stat.) ± 4.4 (syst.) pb and σ${t-ch.}$ $ \left(\overline{t}\right) $ = 27.6 ± 1.3 (stat.) ± 3.7 (syst.) pb, respectively. The measured ratio of cross sections is R${t-ch.}$ = σ${t-ch.}$(t)/σ${t-ch.}$ $ \left(\overline{\mathrm{t}}\right) $ = 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 $ \sqrt{s} $ = 7 TeV, a value |V${tb}$| = 0.998 ± 0.038 (exp.) ± 0.016 (theo.) is obtained.