Muon-proton mass ratio

$m_μ/mₚ$ = 0.112 609 5262(25)

Value: 0.112 609 5262
Standard uncertainty: 2.5 × 10⁻⁹
Relative uncertainty: 2.2 × 10⁻⁸ (22 parts per billion)
Status: Measured
Symbol: $m_μ/mₚ$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# muon-proton mass ratio, CODATA 2022 (NIST)
muon_proton_mass_ratio = 1.126095262e-1  # standard uncertainty 2.5e-9

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

What it is

The mass of the muon divided by the mass 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	0.112 609 5262(25)	2.2 × 10⁻⁸	−0.1 σ of 2018
2018	0.112 609 5264(25)	2.2 × 10⁻⁸	+0.1 σ of 2014
2014	0.112 609 5262(25)	2.2 × 10⁻⁸	−0.4 σ of 2010
2010	0.112 609 5272(28)	2.5 × 10⁻⁸	+0.4 σ of 2006
2006	0.112 609 5261(29)	2.6 × 10⁻⁸	−0.3 σ of 2002
2002	0.112 609 5269(29)	2.6 × 10⁻⁸	+2.8 σ of 1998
1998	0.112 609 5173(34)	3.0 × 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).