Capacitor fundamental formula

the formula for a simple capacitor is well known,
C = er*eo * area / (distance)


I'm trying to determind the permittivity of a dielectric using a parallel plate capacitor method.
unfortunately i'm not getting accurate results, i did some reading and i came across this.
in some places, there is an extra constant in the capacitance formular.

https://www.edaboard.com/thread164509.html
εr=C*h/(8.84*W*L)

as seen above, there is an extra factor of 8.84

in this literature,
there is extra 0.225 factor.

http://www.ipc.org/4.0_Knowledge/4.1...t/2.5.5.1b.pdf
Permittivity =Cs.t / 0.225A

where:
cs= capacitance in picofarads
t = avg. thickness of specimen in inches
A = effective area of specimen in square inches


are these constant some kind of fringging capacitance correction?
what are they?

Firstly, both these factors are equal. The 8.84 factor is when we take measurements in meters whereas the 0.225 factor is when we take measurements in inches.

As for the 8.84 factor itself, it is the permittivity of free space.

In conclusion, you've got only one formula:

E_r = C * Distance / ( E_o * Area )

Where C is in Farads, E_o is 8.85418782 × 10^-12 m^-3 kg^-1 s⁴ A², Area is in m², and Distance is in meters. This reduces to the first formula you typed first, with 8.85418782 being approximated as 8.84.

Yes, with units of Farads and meters.

That's e0. From Wikipedia:
ε0 ≈ 8.854187817620... × 10−12 farads per metre (F·m−1)


Presumably that's to convert from metric to inches.

my goodness, i never thought that 8.85 is the eo constant. LOL!
but the 0.225, if its eo in inches, shouldn't the value 8.85m-->348.425inch

1 inch = 0.0254 meters
0.0254 * 8.85 = 0.225