Nuclear magneton

$μ_N$ = 5.050 783 7393(16) × 10⁻²⁷ J T⁻¹

Value: 5.050 783 7393 × 10⁻²⁷ J T⁻¹
Standard uncertainty: 1.6 × 10⁻³⁶ J T⁻¹
Relative uncertainty: 3.2 × 10⁻¹⁰ (317 parts per trillion)
Status: Measured
Symbol: $μ_N$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# nuclear magneton, CODATA 2022 (NIST)
mu_N = 5.0507837393e-27  # J T^-1, standard uncertainty 1.6e-36

# SciPy: scipy.constants.physical_constants['nuclear magneton']

What it is

The natural unit for the magnetic moments of nuclei, built like the Bohr magneton but with the proton mass, so it is about 1836.15 times smaller. The proton's own moment is about 2.79 nuclear magnetons.

Equations

$μ_N = eℏ/(2mₚ)$ definition

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	5.050 783 7393(16) × 10⁻²⁷	3.2 × 10⁻¹⁰	−4.5 σ of 2018
2018	5.050 783 7461(15) × 10⁻²⁷	3.0 × 10⁻¹⁰	+1.5 σ of 2014
2014	5.050 783 699(31) × 10⁻²⁷	6.1 × 10⁻⁹	+1.5 σ of 2010
2010	5.050 783 53(11) × 10⁻²⁷	2.2 × 10⁻⁸	+2.2 σ of 2006
2006	5.050 783 24(13) × 10⁻²⁷	2.6 × 10⁻⁸	−0.4 σ of 2002
2002	5.050 783 43(43) × 10⁻²⁷	8.5 × 10⁻⁸	+1.3 σ of 1998
1998	5.050 783 17(20) × 10⁻²⁷	4.0 × 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).