ConstantID

Tau-proton mass ratio

Atomic & nuclearMeasured

mτ/mp = 1.893 76(13)

Value
1.893 76
Standard uncertainty
1.3 × 10−4
Relative uncertainty
6.9 × 10−5 (69 parts per million)
Status
Measured
Symbol
mτ/mp
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# tau-proton mass ratio, CODATA 2022 (NIST)
tau_proton_mass_ratio = 1.89376  # standard uncertainty 0.00013

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

What it is

The mass of the tau 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).

tau-proton mass ratio: CODATA values 1998–2022 relative to the 2022 value, in parts per million, with one-standard-uncertainty bars−200−1000+100+200parts per million1998200220062010201420182022

Relative uncertainty

tau-proton mass ratio: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻⁵10⁻⁴10⁻³1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20221.893 76(13)6.9 × 10−5 +0.0 σ of 2018
20181.893 76(13)6.9 × 10−5 +0.2 σ of 2014
20141.893 72(17)9.0 × 10−5 +0.0 σ of 2010
20101.893 72(17)9.0 × 10−5 −0.6 σ of 2006
20061.893 90(31)1.6 × 10−4 +0.0 σ of 2002
20021.893 90(31)1.6 × 10−4 −0.2 σ of 1998
19981.893 96(31)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).

Related constants

Atomic & nuclear λ¯C,τ Reduced tau Compton wavelength 1.110 538(75) × 10−16 m Atomic & nuclear λC,τ Tau Compton wavelength 6.977 71(47) × 10−16 m Atomic & nuclear mτ/me Tau-electron mass ratio 3477.23(23) Atomic & nuclear mτc2 Tau energy equivalent 1776.86(12) MeV Atomic & nuclear mτ Tau mass 3.167 54(21) × 10−27 kg Atomic & nuclear mτc2 Tau mass energy equivalent 2.846 84(19) × 10−10 J Atomic & nuclear mτ Tau mass in u 1.907 54(13) u Atomic & nuclear M(τ) Tau molar mass 1.907 54(13) × 10−3 kg mol−1