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.