Proton rms charge radius

$r_{p}$ = 8.4075(64) × 10⁻¹⁶ m

Value: 8.4075 × 10⁻¹⁶ m
Standard uncertainty: 6.4 × 10⁻¹⁹ m
Relative uncertainty: 7.6 × 10⁻⁴ (761 parts per million)
Status: Measured
Symbol: $r_{p}$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# proton rms charge radius, CODATA 2022 (NIST)
proton_rms_charge_radius = 8.4075e-16  # m, standard uncertainty 6.4e-19

# SciPy: scipy.constants.physical_constants['proton rms charge radius']

What it is

The root-mean-square radius of the proton's electric charge distribution, about 0.84 femtometres. In 2010 measurements with muonic hydrogen gave a value 4% smaller than electron scattering and hydrogen spectroscopy had: the “proton radius puzzle”. The chart below shows how CODATA's value moved as new hydrogen measurements agreed with the smaller one.

Equations

$rₚ = √(⟨r²⟩)$ definition

In other units

Unit	Value
CGS (cm)	8.4075 × 10⁻¹⁴
fm femtometre	0.840 75

Converted with ConstantID's unit table; digits are rounded to the precision of the value, and a long exact value is rounded only for display. The relative uncertainty is unchanged by conversion to an exactly defined unit.

How the value changed, 1998–2022

Each point is one CODATA adjustment, plotted as its difference from the 2022 value; the bars show one standard uncertainty (an arrowhead means the bar runs off the chart).

Relative uncertainty

CODATA	Value (uncertainty)	Relative uncertainty	Change from previous
2022	8.4075(64) × 10⁻¹⁶	7.6 × 10⁻⁴	−0.3 σ of 2018
2018	8.414(19) × 10⁻¹⁶	2.3 × 10⁻³	−5.5 σ of 2014
2014	0.8751(61) × 10⁻¹⁵	7.0 × 10⁻³	−0.5 σ of 2010
2010	0.8775(51) × 10⁻¹⁵	5.8 × 10⁻³	+0.1 σ of 2006
2006	0.8768(69) × 10⁻¹⁵	7.9 × 10⁻³	+0.3 σ of 2002
2002	0.8750(68) × 10⁻¹⁵	7.8 × 10⁻³

“Change from previous” is the shift in the value divided by the standard uncertainty of the previous adjustment. Earlier values are converted into the current unit where NIST changed it (for example J s to J Hz⁻¹).