Muon-proton magnetic moment ratio

$μ_μ/μₚ$ = −3.183 345 146(71)

Value: −3.183 345 146
Standard uncertainty: 7.1 × 10⁻⁸
Relative uncertainty: 2.2 × 10⁻⁸ (22 parts per billion)
Status: Measured
Symbol: $μ_μ/μₚ$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# muon-proton magnetic moment ratio, CODATA 2022 (NIST)
muon_proton_magnetic_moment_ratio = -3.183345146  # standard uncertainty 7.1e-8

# SciPy: scipy.constants.physical_constants['muon-proton mag. mom. ratio']

What it is

The magnetic moment of the muon divided by the magnetic moment of the 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	−3.183 345 146(71)	2.2 × 10⁻⁸	−0.1 σ of 2018
2018	−3.183 345 142(71)	2.2 × 10⁻⁸	+0.0 σ of 2014
2014	−3.183 345 142(71)	2.2 × 10⁻⁸	−0.4 σ of 2010
2010	−3.183 345 107(84)	2.6 × 10⁻⁸	+0.4 σ of 2006
2006	−3.183 345 137(85)	2.7 × 10⁻⁸	−0.2 σ of 2002
2002	−3.183 345 118(89)	2.8 × 10⁻⁸	+2.7 σ of 1998
1998	−3.183 345 39(10)	3.1 × 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).