This is the rms electric charge radius, $\sqrt {\langle r{}^{2}_{E}\rangle }$.

There are three kinds of measurements of the proton radius: via transitions in atomic hydrogen; via electron scattering off hydrogen; and via muonic hydrogen Lamb shift. Most measurements of the radius of the proton involve electron-proton interactions, the most recent of which is the electron scattering measurement XIONG 2019, and the atomic-hydrogen result BEZGINOV 2019. These can be compared to another atomic-hydrogen value BEYER 2017 and with the best measurement using muonic hydrogen Lamb shift ANTOGNINI 2013, that is far more precise.

The latest 2022 CODATA recommendation (MOHR 2025) is based on much improved theory descriptions for muonic hydrogen Lamb shift and the atomic-hydrogen transitions. MOHR 2025 do not include the electron scattering data because of a lack of consensus as to how the electron-scattering data should be analyzed, and there remains some tension between the different r$_{p}$ measurements. See GAO 2022A for an updated discussion.

See our 2014 edition (Chinese Physics C38 070001 (2014)) for values published before 2003.

S016CR VALUE (fm) DOCUMENT ID TECN  COMMENT $0.84075$ $\pm0.00064$ 1 MOHR 2025   RVUE 2022 CODATA • • We do not use the following data for averages, fits, limits, etc. • • $0.847$ $\pm0.008$ 2 CUI 2021   FIT use existing ${{\mathit e}}{{\mathit p}}$ data $0.878$ $\pm0.011$ $\pm0.031$ 3 MIHOVILOVIC 2021   ISR ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ reanalysis $0.833$ $\pm0.010$ 4 BEZGINOV 2019   LASR 2S-2P transition in ${}^{}\mathrm {H}$ $0.831$ $\pm0.007$ $\pm0.012$ 5 XIONG 2019   SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor $0.877$ $\pm0.013$ 6 FLEURBAEY 2018   LASR 1S-3S transition in ${}^{}\mathrm {H}$ $0.8335$ $\pm0.0095$ 7 BEYER 2017   LASR 2S-4P transition in ${}^{}\mathrm {H}$ $0.8751$ $\pm0.0061$ MOHR 2016   RVUE 2014 CODATA value $0.895$ $\pm0.014$ $\pm0.014$ 8 LEE 2015   SPEC Just 2010 Mainz data $0.916$ $\pm0.024$ LEE 2015   SPEC World data, no Mainz $0.84087$ $\pm0.00026$ $\pm0.00029$ ANTOGNINI 2013   LASR ${{\mathit \mu}}{{\mathit p}}$-atom Lamb shift $0.8775$ $\pm0.0051$ MOHR 2012   RVUE 2010 CODATA, ${{\mathit e}}{{\mathit p}}$ data $0.875$ $\pm0.008$ $\pm0.006$ ZHAN 2011   SPEC Recoil polarimetry $0.879$ $\pm0.005$ $\pm0.006$ BERNAUER 2010   SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor $0.912$ $\pm0.009$ $\pm0.007$ BORISYUK 2010   reanalyzes old ${{\mathit e}}{{\mathit p}}$ data $0.871$ $\pm0.009$ $\pm0.003$ HILL 2010   z-expansion reanalysis $0.84184$ $\pm0.00036$ $\pm0.00056$ POHL 2010   LASR See ANTOGNINI 2013 $0.8768$ $\pm0.0069$ MOHR 2008   RVUE 2006 CODATA value $0.844$ ${}^{+0.008}_{-0.004}$ BELUSHKIN 2007   Dispersion analysis $0.897$ $\pm0.018$ BLUNDEN 2005   SICK 2003 + 2${{\mathit \gamma}}$ correction $0.8750$ $\pm0.0068$ MOHR 2005   RVUE 2002 CODATA value $0.895$ $\pm0.010$ $\pm0.013$ SICK 2003   ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ reanalysis 1  MOHR 2025 do not include the electron scattering data. 2  CUI 2021 employ a new mathematical procedure (statistical SPM, Schlessinger point method) based on form-unbiased interpolations of existing ${{\mathit e}}{{\mathit p}}$ scattering data. 3  MIHOVILOVIC 2021 reports a value of $0.878$ $\pm0.011$ $\pm0.031$ $\pm0.002$ fm where the last uncertainty comes from the dependence on the model form factor function. 4  BEZGINOV 2019 measures the 2${{\mathit S}_{{{1/2}}}}$ to 2${{\mathit P}_{{{1/2}}}}$ transition frequency in atomic hydrogen using the frequency-offset separated oscillatory field (FOSOF) technique. The result agrees well with the muonic hydrogen Lamb shift value. 5  The XIONG 2019 value from ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ scattering and supports the muonic hydrogen Lamb shift value. 6  FLEURBAEY 2018 measures the 1S-3S transition frequency in hydrogen and in combination with the 1S-2S transition frequency deduces the proton radius and the Rydberg constant. 7  The BEYER 2017 result is 3.3 combined standard deviations below the MOHR 2016 (2014 CODATA) value. The experiment measures the 2S-4P transition in hydrogen and gets the proton radius and the Rydberg constant. 8  Authors also provide values for combinations of all available data.

References