${{\mathit p}}$ CHARGE RADIUS INSPIRE search

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:
MOHR 2025
RMP 97 025002 CODATA Recommended Values of the Fundamental Physical Constants: 2022
CUI 2021
PRL 127 092001 Fresh Extraction of the Proton Charge Radius from Electron Scattering
MIHOVILOVIC 2021
EPJ A57 107 The proton charge radius extracted from the initial-state radiation experiment at MAMI
BEZGINOV 2019
SCI 365 1007 A measurement of the atomic hydrogen Lamb shift and the proton charge radius
XIONG 2019
NAT 575 147 A small proton charge radius from an electron?proton scattering experiment
FLEURBAEY 2018
PRL 120 183001 New Measurement of the $1S-3S$ Transition Frequency of Hydrogen: Contribution to the Proton Charge Radius Puzzle
BEYER 2017
SCI 358 79 The Rydberg Constant and Proton Size from Atomic Hydrogen
MOHR 2016
RMP 88 035009 CODATA Recommended Values of the Fundamental Physical Constants: 2014
LEE 2015
PR D92 013013 Extraction of the Proton Radius from Electron-Proton Scattering Data
ANTOGNINI 2013
SCI 339 417 Proton Structure from the Measurement of 2$\mathit S−2\mathit P$ Transition Frequencies of Muonic Hydrogen
MOHR 2012
RMP 84 1527 CODATA Recommended Values of the Fundamental Physical Constants: 2010
ZHAN 2011
PL B705 59 High-Precision Measurement of the Proton Elastic Form Factor Ratio $\mathit \mu _{p}G_{E}/G_{M}$ at low $\mathit Q{}^{2}$
BERNAUER 2010
PRL 105 242001 High-Precision Determination of the Electric and Magnetic Form Factors of the Proton
Also
PR C90 015206 Electric and Magnetic Form Factors of the Proton
BORISYUK 2010
NP A843 59 Proton Charge and Magnetic rms Radii from the Elastic ${{\mathit e}}{{\mathit p}}$ Scattering data
HILL 2010
PR D82 113005 Model Independent Extraction of the Proton Charge Radius from Electron Scattering
POHL 2010
NAT 466 213 The Size of the Proton
MOHR 2008
RMP 80 633 CODATA Recomended Values of the Fundamental Physical Constants: 2006
BELUSHKIN 2007
PR C75 035202 Dispersion Analysis of the Nucleon Form Factors Including Meson Continua
BLUNDEN 2005
PR C72 057601 Proton Radii and Two-Photon Exchange
MOHR 2005
RMP 77 1 NIST Constants
SICK 2003
PL B576 62 On the rms-Radius of the Proton