Vacuum magnetic permeability
UniversalMeasured
= 1.256 637 061 27(20) × 10−6 N A−2
- Value
- 1.256 637 061 27 × 10−6 N A−2
- Standard uncertainty
- 2 × 10−16 N A−2
- Relative uncertainty
- 1.6 × 10−10 (159 parts per trillion)
- Status
- Measured since 2019 (exact before)
- Symbol
- Source
- CODATA 2022 via NIST · NIST entry
Use in a calculation
# vacuum magnetic permeability, CODATA 2022 (NIST)
mu_0 = 1.25663706127e-6 # N A^-2, standard uncertainty 2e-16
# SciPy: scipy.constants.physical_constants['vacuum mag. permeability']What it is
The magnetic constant μ₀ sets the strength of magnetic forces between currents. Before 2019 it was exactly 4π × 10⁻⁷ N/A² by definition of the ampere. Now the elementary charge is fixed instead, μ₀ = 2αh/(e²c) is measured through the fine-structure constant, and it differs from 4π × 10⁻⁷ by 0.13 parts per billion.
Until CODATA 2014 this value was exact by definition. Since the 2019 SI redefinition it is measured, because the constant that used to fix it was replaced by a fixed elementary charge.
Equations
- since 2019
- with the electric constant
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 | 1.256 637 061 27(20) × 10−6 | 1.6 × 10−10 | −4.5 σ of 2018 |
| 2018 | 1.256 637 062 12(19) × 10−6 | 1.5 × 10−10 | |
| 2014 | 12.566 370 614… × 10−7 | exact | exact |
| 2010 | 12.566 370 614… × 10−7 | exact | exact |
| 2006 | 12.566 370 614… × 10−7 | exact | exact |
| 2002 | 12.566 370 614… × 10−7 | exact | exact |
| 1998 | 1 256 637.061 435 917… | exact |
“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).