  We have determined the proton and the neutron charge radii from a global
analysis of the proton and the neutron elastic form factors, after first
performing a flavor decomposition of these form factors under charge symmetry
in the light cone frame formulation. We then extracted the transverse
mean-square radii of the flavor dependent quark distributions. In turn, these
are related in a model-independent way to the proton and neutron charge radii
but allow us to take into account motion effects of the recoiling nucleon for
data at finite but high momentum transfer. In the proton case we find $\langle
r_p \rangle = 0.852 \pm0.002_{\rm (stat.)} \pm0.009_{\rm (syst.)}~({\rm fm})$,
consistent with the proton charge radius obtained from muonic hydrogen
spectroscopy \cite{pohl:2010,antog2013}. The current method improves on the
precision of the $\langle r_p \rangle$ extraction based on the form factor
measurements. Furthermore, we find no discrepancy in the $\langle r_p \rangle$
determination among the different electron scattering measurements, all of
which, utilizing the current method of extraction, result in a value that is
consistent with the smallest $\langle r_p \rangle$ extraction from the electron
scattering measurements \cite{Xiong:2019umf}. Concerning the neutron case, past
results relied solely on the neutron-electron scattering length measurements,
which suffer from an underestimation of underlying systematic uncertainties
inherent to the extraction technique. Utilizing the present method we have
performed the first extraction of the neutron charge radius based on nucleon
form factor data, and we find $\langle r_n^2 \rangle = -0.122 \pm0.004_{\rm
(stat.)} \pm0.010_{\rm (syst.)}~({\rm fm}^2)$.
