The normalized differential cross section for top-quark pair production in association with at least one jet is studied as a function of the inverse of the invariant mass of the $$ t\overline{t} $$ + 1-jet system. This distribution can be used for a precise determination of the top-quark mass since gluon radiation depends on the mass of the quarks. The experimental analysis is based on proton-proton collision data collected by the ATLAS detector at the LHC with a centre-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.6 fb−1. The selected events were identified using the lepton+jets top-quark-pair decay channel, where lepton refers to either an electron or a muon. The observed distribution is compared to a theoretical prediction at next-to-leading-order accuracy in quantum chromodynamics using the pole-mass scheme. With this method, the measured value of the top-quark pole mass, m pole , is: $$ {m}_t^{\mathrm{pole}}=173.7\pm 1.5\left(\mathrm{stat}.\right)\pm 1.4{\left(\mathrm{syst}.\right)}_{-0.5}^{+1.0}\left(\mathrm{theory}\right)\mathrm{GeV}. $$ This result represents the most precise measurement of the top-quark pole mass to date.