  Constraints from analyticity are combined with experimental electron-proton
scattering data to determine the proton charge radius. In contrast to previous
determinations, we provide a systematic procedure for analyzing arbitrary data
without model-dependent assumptions on the form factor shape. We also
investigate the impact of including electron-neutron scattering data, and
$\pi\pi\to N\bar{N}$ data. Using representative datasets we find r_E^p=0.870
+/- 0.023 +/- 0.012 fm using just proton scattering data;
r_E^p=0.880^{+0.017}_{-0.020} +/- 0.007 fm adding neutron data; and r_E^p=0.871
+/- 0.009 +/- 0.002 +/- 0.002 fm adding $\pi\pi$ data. The analysis can be
readily extended to other nucleon form factors and derived observables.
