Coulombs law for electrostatic force between two pointcharges and Newtons law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses. Compare the strength of these forces by determining the ratio of their magnitudes for an electron and a proton.
The electric force between an electron and a proton at a distance r apart is:
$F_e=-\frac{e^2}{4\pi {ϵ}_0{r}^2}$
where the negative sign indicates that the force is attractive. The corresponding gravitational force (always attractive) is
$F_G=-G\frac{m_p{m}_e}{r^2}$
where $m_p$ and $m_e$ are the masses of a proton and an electron respectively.
$|\frac{F_e}{F_G}|=\frac{e^2}{4\pi {ϵ}_{0}G{m}_p{m}_e}=2.4\times 10^{39}$