# Comparing the strength of gravity and electricity

Yes, they can. Both interactions can be modeled using perturbative quantum field theory, where their strength is parametrized by a dimensionless coupling constant.

Electromagnetic repulsion between two electrons can be written as a power series in $$\alpha$$, the fine structure constant, which is dimensionless and has a value of roughly 1/137.

Meanwhile, the gravitational attraction between two electrons can be expanded in a similar way in a power series in $$\alpha_G$$, which is a dimensionless constant with a value of roughly $$10^{-45}$$.

The precise value of $$\alpha_G$$ depends somewhat on which particle you're comparing, since ultimately it's the square of the ratio of the particle's mass to the Planck mass. However, for fundamental particles, this ratio does not vary by more than ten orders of magnitude, which still places $$\alpha_G$$ far smaller than $$\alpha$$ no matter which fundamental particle you choose to compare.