> [!significance] Metadata > Author:: [Vatsal Sanjay](https://vatsalsanjay.com)<br> > Date published:: Jan 21, 2025<br> > Date modified:: Jan 21, 2025 at 11:05 CET # Permittivity of free space In Gauss’s law, $\varepsilon$ the permittivity of free space. It quantifies how an electric field propagates through a vacuum. In the standard form of Gauss’s law, $\oint \mathbf{E}\cdot d\mathbf{A} \;=\; \frac{Q_{\text{enc}}}{\varepsilon_0},$ appears as the proportionality constant relating the net electric flux through a closed surface to the total charge enclosed. Numerically, $\varepsilon_0 \approx 8.854 \times 10^{-12}\,\mathrm{F/m}$. It also factors into the relationship between the speed of light $c$, the vacuum permeability $\mu_0$, and itself, via $c = \frac{1}{\sqrt{\varepsilon_0\,\mu_0}}$.