Modern direct measurements are based on precision measurements of the atomic energy levels in hydrogen and deuterium, and measurements of scattering of electrons by nuclei. There is most interest in knowing the charge radii of protons and deuterons, as these can be compared with the spectrum of atomic hydrogen and deuterium: the nonzero size of the nucleus causes a shift in the electronic energy levels which shows up as a change in the frequency of the spectral lines. Such comparisons are a test of quantum electrodynamics (QED).
Since 2002, the proton and deuteron charge radii have been independently refined parameters in the CODATA set of recommended values for physical constants. Both scattering data and spectroscopic data are used to determine the recommended values. Furthermore, spectroscopic measurements can be made both with regular hydrogen (consisting of a proton and an electron) or muonic hydrogen (an exotic atom consisting of a proton and a negative muon). An inconsistency between proton charge radius measurements made using different techniques was known as the proton radius puzzle, but more recent measurements show consistent results.
The 2018 CODATA recommended values are:
:proton: R = 8.414(19)×10 m
:deuteron: R = 2.127 99(74)×10 m