Measurements of fiducial integrated and differential cross sections for inclusive $$W^+$$ , $$W^-$$ and Z boson production are reported. They are based on $$25.0 \pm 0.5\; \mathrm {pb}^{-1}$$ of pp collision data at $$\sqrt{s} = 5.02$$ TeV collected with the ATLAS detector at the CERN Large Hadron Collider. Electron and muon decay channels are analysed, and the combined $$W^+$$ , $$W^-$$ and Z integrated cross sections are found to be $$\sigma _{W^+}= 2266 \pm 9~\text {(stat)} \pm 29~\text {(syst)} \pm 43~\text {(lumi)}$$ pb, $$\sigma _{W^-}= 1401 \pm 7~\text {(stat)} \pm 18~\text {(syst)} \pm 27~\text {(lumi)}$$ pb, and $$\sigma _Z= 374.5 \pm 3.4~\text {(stat)} \pm 3.6~\text {(syst)} \pm 7.0~\text {(lumi)}$$ pb, in good agreement with next-to-next-to-leading-order QCD cross-section calculations. These measurements serve as references for Pb+Pb interactions at the LHC at $$\sqrt{s_{\mathrm {NN}}}=5.02$$ TeV.