Electron to shielded proton magnetic moment ratio

$μₑ/μₚ′$ = −658.227 5856(27)

Value: −658.227 5856
Standard uncertainty: 2.7 × 10⁻⁶
Relative uncertainty: 4.1 × 10⁻⁹ (4.1 parts per billion)
Status: Measured
Symbol: $μₑ/μₚ′$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# electron to shielded proton magnetic moment ratio, CODATA 2022 (NIST)
electron_to_shielded_proton_magnetic_mom = -6.582275856e2  # standard uncertainty 2.7e-6

# SciPy: scipy.constants.physical_constants['electron to shielded proton mag. mom. ratio']

What it is

The magnetic moment of the electron divided by the magnetic moment of the shielded proton. Ratios like this are often measured more precisely than either quantity on its own, which is why CODATA lists them.

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	−658.227 5856(27)	4.1 × 10⁻⁹	+1.6 σ of 2018
2018	−658.227 5971(72)	1.1 × 10⁻⁸	+0.0 σ of 2014
2014	−658.227 5971(72)	1.1 × 10⁻⁸	+0.0 σ of 2010
2010	−658.227 5971(72)	1.1 × 10⁻⁸	+0.0 σ of 2006
2006	−658.227 5971(72)	1.1 × 10⁻⁸	−0.2 σ of 2002
2002	−658.227 5956(71)	1.1 × 10⁻⁸	−0.0 σ of 1998
1998	−658.227 5954(71)	1.1 × 10⁻⁸

“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).