How do you calculate the pull force of an electromagnet with an iron core

I'm surprised Nef that no answer yet. I suspect it isn't a linear relationship with current and no. of turns but you might try Googling

http://www.ehow.com/how_5969962_calculate-force-electromagnet.html

Off cource there is a direct relation with iron core tip area and the pull force of an electromagnet, since the basic formula includes the area of the core tip. Many people taking this area as the cross section area of the entire electromagnet (i.e coil). THIS IS WRONG.
Technicians and manufactures offen use this formula
CoreΦ(cm)=sqrt((2*Kgr)/(33,8)).
Anyway, this is the first parameter to calculate in designing of an electroagnet, espesially when the application is to lift vertically or to levitate a ferous object.
This is not an empirical formula, but I have no time to go further.

Sorry but the correct formula is
CoreΦ(cm)=2*sqrt((2*Kgr)/33,8)
For example if you want a design a DC e/m to act on a mass of 100gr at a distance of 10 cm, then you need a soft iron core with Φ 2,3 cm to work with a flux density of 1,53T. In this case, the length of core sould be about 21 cm. This is not the optimum design anyway....This e/m can hold a mass of 20Kgr.
Tip geometry plays a role but minor.
Core also plays role on the e/m thermodynamics since the heat flow is about the half to the core, and the rate is 0,0045W/cm^2/oC
Do not be generous with core dimensions. All the time try to select the minimum required.

actual force calculation formula
F = 0.051 *A(area of core in mtr)*Bm^2/4*pi*10^(-7)

from above formula Bm required to pull 20KG load is of 0.31T,A=0.023*0.21

Papa thank you