This paper presents the electron and photon energy calibration obtained with the ATLAS detector using 140 fb-1 of LHC proton-proton collision data recorded at √(s) = 13 TeV between 2015 and 2018. Methods for the measurement of electron and photon energies are outlined, along with the current knowledge of the passive material in front of the ATLAS electromagnetic calorimeter. The energy calibration steps are discussed in detail, with emphasis on the improvements introduced in this paper. The absolute energy scale is set using a large sample of Z-boson decays into electron-positron pairs, and its residual dependence on the electron energy is used for the first time to further constrain systematic uncertainties. The achieved calibration uncertainties are typically 0.05% for electrons from resonant Z-boson decays, 0.4% at E T ∼ 10 GeV, and 0.3% at E T ∼ 1 TeV; for photons at E T ∼ 60 GeV, they are 0.2% on average. This is more than twice as precise as the previous calibration. The new energy calibration is validated using J/ψ → ee and radiative Z-boson decays.