This paper presents the muon momentum calibration and performance studies for the ATLAS detector based on the pp collisions data sample produced at $\sqrt{s}$ = 13 TeV at the LHC during Run 2 and corresponding to an integrated luminosity of 139 ${\textrm{fb}}^{-1}$. An innovative approach is used to correct for potential charge-dependent momentum biases related to the knowledge of the detector geometry, using the $Z\rightarrow \mu ^{+}\mu ^{-}$ resonance. The muon momentum scale and resolution are measured using samples of $J/\psi \rightarrow \mu ^{+}\mu ^{-}$ and $Z\rightarrow \mu ^{+}\mu ^{-}$ 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 $\Upsilon \rightarrow \mu ^{+}\mu ^{-}$ 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 ${\textrm{TeV}}^{-1}$.