Muon-tau mass ratio

$m_μ/m_τ$ = 5.946 35(40) × 10⁻²

Value: 5.946 35 × 10⁻²
Standard uncertainty: 4 × 10⁻⁶
Relative uncertainty: 6.7 × 10⁻⁵ (67 parts per million)
Status: Measured
Symbol: $m_μ/m_τ$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# muon-tau mass ratio, CODATA 2022 (NIST)
muon_tau_mass_ratio = 5.94635e-2  # standard uncertainty 4e-6

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

What it is

The mass of the muon divided by the mass of the tau. 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	5.946 35(40) × 10⁻²	6.7 × 10⁻⁵	+0.0 σ of 2018
2018	5.946 35(40) × 10⁻²	6.7 × 10⁻⁵	−0.3 σ of 2014
2014	5.946 49(54) × 10⁻²	9.1 × 10⁻⁵	+0.0 σ of 2010
2010	5.946 49(54) × 10⁻²	9.1 × 10⁻⁵	+0.6 σ of 2006
2006	5.945 92(97) × 10⁻²	1.6 × 10⁻⁴	+0.0 σ of 2002
2002	5.945 92(97) × 10⁻²	1.6 × 10⁻⁴	+0.2 σ of 1998
1998	5.945 72(97) × 10⁻²	1.6 × 10⁻⁴

“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).