The problem is to calculate an inductor. If everything (inductivity, number of turns, core crossection, permeability,  magnetic length ... ) is given expect the length of the air-gap. It seams to be easy to calculate the length of it.

I calculate the air gap with a formula called "Effective Permeability" but it does not recognize the fringe field.

Is there an analytical way to calculate the air gap more precise?

Thanks for helping, kind regards Tobi