  We present a precise calculation of the pion form factor using overlap
fermions on seven ensembles of 2+1-flavor domain-wall configurations with pion
masses varying from 139 to 340 MeV. Taking advantage of the fast Fourier
transform and other techniques to access many combinations of source and sink
momenta, we find the pion mean square charge radius to be $\langle {r_\pi^2}
\rangle= 0.430(5)(13)\ {\rm{fm^2}}$, which agrees well with the experimental
result, and includes the systematic uncertainties from chiral extrapolation,
lattice spacing and finite-volume dependence. We also find that $\langle
{r_\pi^2} \rangle$ depends on both the valence and sea quark masses strongly
and predict the pion form factor up to $Q^2 = 1.0 \ {\rm{GeV^2}}$ which agrees
with experiments very well.
