This paper presents the muon momentum calibration and performance studies for the ATLAS detector based on the pp collisions data sample produced at root s = 13 TeV at the LHC during Run 2 and corresponding to an integrated luminosity of 139 fb(-1). An innovative approach is used to correct for potential charge-dependent momentum biases related to the knowledge of the detector geometry, using the Z ->mu(+)mu(-) resonance. The muon momentum scale and resolution are measured using samples of J/psi ->mu(+)mu(-) and Z ->mu(+)mu(-) events. A calibration procedure is defined and applied to simulated data to match the performance measured in real data. The calibration is validated using an independent sample of Upsilon ->mu(+)mu(-) events. At the Z(J/psi) peak, the momentum scale is measured with an uncertainty at the 0.05% (0.1%) level, and the resolution is measured with an uncertainty at the 1.5% (2%) level. The charge-dependent bias is removed with a dedicated in situ correction for momenta up to 450 GeV with a precision better than 0.03 TeV-1.