Advanced Theory Equations:

Most inductance for a cylinder coil.

    R = 10 / 9 * B   R is radius and B is length of the coil.

Most inductance for a pancake coil.

    R = 11 / 8 * W   R is the mean radius and W is the inner radius minus the outer radius.

Same symbols as below in physics, all units from here on are in SI.

p stands for primary, s stands for secondary.

Cp = i / (2 * Pi * fp * Vp)

fs  =  c / (4 * length of secondary wire)

Lp = 1 / (4 * Pi * Pi * Cp)

Ls = ((rs * N) * (rs * N)) / (9 * rs + 10 * Height)    rs : secondary radius

Cs = (Lp * Cp) / Ls

Np = sqrt(Lp * (8 * mean radius + 11 * difference in (min and max) coil radius)) / mean radius