Inverse fine-structure constant

$α^ − 1$ = 137.035 999 177(21)

Value: 137.035 999 177
Standard uncertainty: 2.1 × 10⁻⁸
Relative uncertainty: 1.5 × 10⁻¹⁰ (153 parts per trillion)
Status: Measured
Symbol: $α^ − 1$
Source: CODATA 2022 via NIST · NIST entry

Use in a calculation

# inverse fine-structure constant, CODATA 2022 (NIST)
inverse_fine_structure_constant = 1.37035999177e2  # standard uncertainty 2.1e-8

# SciPy: scipy.constants.physical_constants['inverse fine-structure constant']

What it is

The reciprocal of the fine-structure constant, the famous “137”. It is the same measured quantity as α, written the other way up.

Equations

$α^ − 1 = 4πε₀ℏc/e²$ 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	137.035 999 177(21)	1.5 × 10⁻¹⁰	+4.4 σ of 2018
2018	137.035 999 084(21)	1.5 × 10⁻¹⁰	−1.8 σ of 2014
2014	137.035 999 139(31)	2.3 × 10⁻¹⁰	+1.5 σ of 2010
2010	137.035 999 074(44)	3.2 × 10⁻¹⁰	−6.4 σ of 2006
2006	137.035 999 679(94)	6.9 × 10⁻¹⁰	+1.2 σ of 2002
2002	137.035 999 11(46)	3.4 × 10⁻⁹	−1.3 σ of 1998
1998	137.035 999 76(50)	3.6 × 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).