  We present a novel method for extracting the proton radius from elastic
electron-proton ($ep$) scattering data. The approach is based on interpolation
via continued fractions augmented by statistical sampling and avoids any
assumptions on the form of function used for the representation of data and
subsequent extrapolation onto $Q^2\simeq 0$. Applying the method to extant
modern $ep$ data sets, we find that all results are mutually consistent and,
combining them, arrive at $r_p=0.847(8)\,$fm. This result compares favourably
with values obtained from contemporary measurements of the Lamb shift in muonic
hydrogen, transitions in electronic hydrogen, and muonic deuterium
spectroscopy.
