  Using dispersion theory with an improved description of the two-pion
continuum based on the precise Roy-Steiner analysis of pion-nucleon scattering,
we analyze recent data from electron-proton scattering. This allows for a
high-precision determination of the electric and magnetic radius of the proton,
$r_E = (0.838^{+0.005}_{-0.004}{}^{+0.004}_{-0.003})\,$fm and $r_M =
(0.847\pm{0.004}\pm{0.004})\,$fm, where the first error refers to the fitting
procedure using bootstrap and the data while the second one refers to the
systematic uncertainty related to the underlying spectral functions.
