Vacuum electric permittivity
UniversalMeasured
= 8.854 187 8188(14) × 10−12 F m−1
- Value
- 8.854 187 8188 × 10−12 F m−1
- Standard uncertainty
- 1.4 × 10−21 F m−1
- Relative uncertainty
- 1.6 × 10−10 (158 parts per trillion)
- Status
- Measured since 2019 (exact before)
- Symbol
- Source
- CODATA 2022 via NIST · NIST entry
Use in a calculation
# vacuum electric permittivity, CODATA 2022 (NIST)
epsilon_0 = 8.8541878188e-12 # F m^-1, standard uncertainty 1.4e-21
# SciPy: scipy.constants.physical_constants['vacuum electric permittivity']What it is
The electric constant ε₀ sets the strength of the electric force between charges in Coulomb's law. It equals 1/(μ₀c²), so since the 2019 redefinition it is a measured quantity with the same relative uncertainty as μ₀ and the fine-structure constant.
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
- Coulomb's law
- with the magnetic 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 | 8.854 187 8188(14) × 10−12 | 1.6 × 10−10 | +4.6 σ of 2018 |
| 2018 | 8.854 187 8128(13) × 10−12 | 1.5 × 10−10 | |
| 2014 | 8.854 187 817… × 10−12 | exact | exact |
| 2010 | 8.854 187 817… × 10−12 | exact | exact |
| 2006 | 8.854 187 817… × 10−12 | exact | exact |
| 2002 | 8.854 187 817… × 10−12 | exact | exact |
| 1998 | 8.854 187 817… × 10−12 | 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).