Proton-electron mass ratio

$mₚ/mₑ$ = 1836.152 673 426(32)

Value: 1836.152 673 426
Standard uncertainty: 3.2 × 10⁻⁸
Relative uncertainty: 1.7 × 10⁻¹¹ (17 parts per trillion)
Status: Measured
Symbol: $mₚ/mₑ$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# proton-electron mass ratio, CODATA 2022 (NIST)
proton_electron_mass_ratio = 1.836152673426e3  # standard uncertainty 3.2e-8

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

What it is

How many times heavier the proton is than the electron. Precision spectroscopy of hydrogen molecular ions measures it directly; astronomers use distant molecules to check that it has not changed over cosmic time.

Equations

$μ = mₚ/(mₑ)$ 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	1836.152 673 426(32)	1.7 × 10⁻¹¹	−0.0 σ of 2018
2018	1836.152 673 43(11)	6.0 × 10⁻¹¹	−2.7 σ of 2014
2014	1836.152 673 89(17)	9.3 × 10⁻¹¹	+1.9 σ of 2010
2010	1836.152 672 45(75)	4.1 × 10⁻¹⁰	−0.0 σ of 2006
2006	1836.152 672 47(80)	4.4 × 10⁻¹⁰	−0.2 σ of 2002
2002	1836.152 672 61(85)	4.6 × 10⁻¹⁰	+1.3 σ of 1998
1998	1836.152 6675(39)	2.1 × 10⁻⁹

“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).