Calculating inductance of Pancake coils (flat spiral coils) with a steel core?

I am trying to build a transformer which contains pancake coils. I need to find a formula(s) to compute the pancake coils inductance with a core of a certain permeability.

I have found many pancake (flat spiral) coil inductance calculators and formulas for air cores, but I need to be able to calculate for ferrite and steel cores.

Thanks for the help!