The quick-&-dirty way is to look in "Machinery's Handbook" in the section entitled "Mechanics". The basic formulas, per "Machinery's Handbook" for force produced by threads depends on whether the thread is jacking/raising or lowering the load.
A screw thread is basically an inclined plane wrapped around a cylinder. The force of the thread against the nut is the action of a wedge. Figuring the mechanical advantage produced by it amounts to stuff you may have learned in HS Physics- having to figure the angle the inclined plane makes to the horizontal and playing with some trig and vectors along with the coefficient of friction. The formulas in "Machinery's Handbook" cut to the chase.
The formulas are too lengthy to type out here, but you will need to know the coefficient of friction between the nut and screw (obtained elsewhere in the Machinery's Handbook). the formulas calculate the force, F, required on a lever of length R, to move a given load Q with a screw thread, having a coefficient of friction Mu- (no Greek letters on this computer) between the nut and screw.
If you do not already own a copy of "Machinery's Handbook", I would strongly reocmmend you get hold of one. Even an old edition will have what amounts to priceless and timeless information.
Joe Michaels