Is there any equation that calculates the $C_d$ value in the formula of air drag ? $$F_d = \rho C_d v^2 A$$ I have found that there are tables for this constant but I am looking for the equation that evalutes it.
$C_d$ has to depend on the fluid, the surface shape, and texture of the object. In addition, that formula is only valid in the laminar flow regime, so when $v$ is sufficient to cause turbulent eddies, you get different behavior. You need to read up on Reynolds numbers and so on.