A measurement of the mass of the W boson is presented based on proton–proton collision data recorded in 2011 at a centre-of-mass energy of 7 TeV with the ATLAS detector at the LHC, and corresponding to $$4.6~\hbox {fb}^{-1}$$ $4.6{\text{fb}}^{-1}$ of integrated luminosity. The selected data sample consists of $$7.8\times 10^6$$ $7.8\times {10}^6$ candidates in the $$W\rightarrow \mu \nu $$ $W\to \mu \nu$ channel and $$5.9\times 10^6$$ $5.9\times {10}^6$ candidates in the $$W\rightarrow e \nu $$ $W\to e\nu$ channel. The W-boson mass is obtained from template fits to the reconstructed distributions of the charged lepton transverse momentum and of the W boson transverse mass in the electron and muon decay channels, yielding $$\begin{aligned} \nonumber m_W = 80370&\pm 7~(\text {stat.}) \pm 11 (\text {exp. syst.}) \\&\pm 14~(\text {mod. syst.})~\text {MeV} \\ = 80370&\pm 19\,\text {MeV}, \end{aligned}$$ $\begin{array}{cc}{m}_W=80370& \pm 7\left(\text{stat.}\right)\pm 11\left(\text{exp. syst.}\right)\\ & \pm 14\left(\text{mod. syst.}\right)\text{MeV}\\ =80370& \pm 19\text{MeV},\end{array}$ where the first uncertainty is statistical, the second corresponds to the experimental systematic uncertainty, and the third to the physics-modelling systematic uncertainty. A measurement of the mass difference between the $$W^+$$ $W^{+}$ and $$W^-$$ $W^{-}$ bosons yields $$m_{W^+}-m_{W^-} = -\,29 \pm 28$$ $m_{W^{+}}-m_{W^{-}}=-29\pm 28$ MeV.