According to Coulomb's law, the electrostatic force between two point charges is given by $F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2}$. Rearranging this formula for the permittivity of free space ($\varepsilon_0$), we get $\varepsilon_0 = \frac{1}{4\pi F} \frac{q_1 q_2}{r^2}$. Substituting the SI units for charge (C), force (N), and distance (m), the unit of $\varepsilon_0$ is $\frac{\text{C} \cdot \text{C}}{\text{N} \cdot \text{m}^2} = \text{C}^2 \text{ N}^{-1} \text{ m}^{-2}$ or $\text{Coulomb}^2 / \text{Newton-metre}^2$.