Magnitude-based PDFF (Proton Density Fat Fraction) and R2∗ mapping with resolved water-fat ambiguity is extended to calculate field inhomogeneity (field map) using the phase images. The estimation is formulated in matrix form, resolving the field map in a least-squares sense. PDFF and R2∗ from magnitude fitting may be updated using the estimated field maps. The limits of quantification of our voxel-independent implementation were assessed. Bland-Altman was used to compare PDFF and field maps from our method against a reference complex-based method on 152 UK Biobank subjects (1.5 T Siemens). A separate acquisition (3 T Siemens) presenting field inhomogeneities was also used. The proposed field mapping was accurate beyond double the complex-based limit range. High agreement was obtained between the proposed method and the reference in UK. Robust field mapping was observed at 3 T, for inhomogeneities over 400 Hz including rapid variation across edges. Field mapping following unambiguous magnitude-based water-fat separation was demonstrated in-vivo and showed potential at 3 T.