K = ?
Have people gotten so lazy that there are free, self-advertising screenshot tools now? There's been the PRTSCR button for over three decades, and MS Paint for about two...
Anyway, some background on transformer physics might be of help?
http://seventransistorlabs.com/tmoranwms/Elec_Magnetics.htmlothers have their preferred references as well.
I distinguish between transformers, which are not intended to store any energy at all, and inductors (coupled or single), which are. (Curiously, a common mode choke is an excellent example of a "transformer", as such, that's used specifically in an inductive fashion.)
For a transformer, the fundamental limitation is, how much flux you can get into a given core. You can put in more flux by adding more turns, but if you can't fit those turns because the wire is too big, you have a problem. Flux is limited, in the worst case, by the saturation property of the material, but in practical cases, may be much less due to heating, especially at higher frequencies.
For an inductor (including coupled inductors), you can calculate based on flux, then calculate required gap based on inductance. The relation Phi_max = Imax * L relates the two quantities. If the core material isn't so easy to control the gap on (you're using pre-gapped cores, open type cores like bobbins, or low-mu materials like powdered iron), then it might be better to calculate from inductance, without concern for flux. (You will have to find flux to calculate losses, though.)
Tim