This paper presents measurements of the ${W}^{+}\to {\mu }^{+}\nu $ and ${W}^{-}\to {\mu }^{-}\nu $ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton–proton collisions at a centre-of-mass energy of 8 $\text{TeV}$ with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of $20.2\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.333333em}{0ex}}\text{fb}{\phantom{\rule{0.333333em}{0ex}}}^{-1}$ . The precision of the cross-section measurements varies between 0.8 and 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.