Background The spatial distribution of charge and magnetization within the proton is encoded in the elastic form factors.These have been precisely measured in elastic electron scattering, and the combination of proton and neutron form factors allows for the separation of the up-and down-quark contributions.Purpose In this work, we extract the proton and neutron form factors from world's data with an emphasis on precise new data covering the low-momentum region, which is sensitive to the large-scale structure of the nucleon. From these, we separate the up-and down-quark contributions to the proton form factors.Method We combine cross section and polarization measurements of elastic electron-proton scattering to separate the proton form factors and two-photon exchange (TPE) contributions. We combine the proton form factors with parameterization of the neutron form factor data and uncertainties to separate the up-and down-quark contributions to the proton's charge and magnetic form factors.Results The extracted TPE corrections are compared to previous phenomenological extractions, TPE calculations, and direct measurements from the comparison of electron and positron scattering. The flavor-separated form factors are extracted and compared to models of the nucleon structure.Conclusions With the inclusion of the precise new data, the extracted TPE contributions show a clear change of sign at low Q 2 , necessary to explain the high-Q 2 form factor discrepancy while being consistent with the known Q 2 → 0 limit. We find that the new Mainz data yield a significantly different result for the proton magnetic form factor and its flavorseparated contributions. We also observe that the RMS radius of both the up-and down-quark distributions are smaller than the RMS charge radius of the proton.