Unofficial
FEMM
documentation
by Dr Stan Zurek

LUA script for calculating magnetic coupling coefficient between two windings. The windings have to be set up as described in the comments in the code below:

-- Short Lua script for calculating coupling factor of two coils.
-- It presumes the problem is already defined in FEMM, and
-- that the two windings are defined by circuits named "pri" and "sec".
-- The problem may be DC or AC at a frequency of your choice.
-- Intended for circuits with series property.
-- Execute with the FEMM menu item File/OpenLuaScript.
clearconsole()
showconsole()
-- Simulate first with only secondary current:
mi_modifycircprop("pri",1,0)
mi_modifycircprop("sec",1,1)
mi_analyze()
mi_loadsolution()
print(mo_getcircuitproperties("sec"))  -- Optional display of intermediate results
print(mo_getcircuitproperties("pri"))  -- Optional display of intermediate results
i, Vsec, Lsec = mo_getcircuitproperties("sec")
i, Vpri_sec, Lpri_sec = mo_getcircuitproperties("pri")
-- Simulate next with only primary current:
mi_modifycircprop("pri",1,1)
mi_modifycircprop("sec",1,0)
mi_analyze()
mi_loadsolution()
print(mo_getcircuitproperties("sec"))  -- Optional display of intermediate results
print(mo_getcircuitproperties("pri"))  -- Optional display of intermediate results
i, Vsec_pri, Lsec_pri = mo_getcircuitproperties("sec")
i, Vpri, Lpri = mo_getcircuitproperties("pri")
-- Calculate and print coupling factor:
coupling_factor = sqrt(Lsec_pri * Lpri_sec / (Lpri * Lsec))
print("Coupling factor is:", coupling_factor)