This paper presents measurements of the W+→μ+ν and W-→μ-ν 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 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2-1. 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.