4π is just a constant. In fact, you will understand the origin of this formula when you go to college. When you say that "the capacitance c of parallel plate capacitors is proportional to the dielectric constant ε, proportional to the opposite area S, and inversely proportional to the distance d between plates", they are only a proportion. It's just a proportional relationship. And after adding 4π, it becomes an equation, so we can know that 3 is another unknown. Having said so much, I wonder if you don't understand this, hehe! ! !

The above is copied online, hehe.

A flat capacitor is composed of two parallel plates (A and B) which are very close to each other. The area of both plates is S. If the two plates are charged with +Q and -Q respectively, the charge density of each plate is σ = q/s. We ignore the edge effect of the plates and regard the electric field between the two plates as a uniform electric field. According to Gauss theorem, the field strength between two plates is E = σ=Q/S ε. =Q/ε.

Then U=∫AB E dl =Ed=Qd/ε. Then according to C=Q/U

It is concluded that C=ε. S/d is the formula of plate capacitance, that is, C=S/4πkd.

Note: ε. = 1/4πk is the vacuum dielectric constant.

The capacitance of a flat capacitor is directly proportional to the area s of the plates and inversely proportional to the distance d between the plates. Capacitance c has nothing to do with whether the capacitor is charged or not, but only with the structure and shape of the capacitor itself.

This is something in college physics. ...