Cable Size

You typically don't calculate cable sizes -- you look them up in a table of standards.

Cable sizes for loads have been determined for copper and aluminum; both common metallic conductors.

Now, for a more in-depth look at it, heat is what determines how much current a conductor can carry, and that depends heavily on the thermodynamics of the application. Copper, for example, has a resistivity (to keep it simple), and I²R_Cu is the power dissipated by a copper conductor. In free air, the heat dissipated by that copper conductor is a function of air temperature and wind speed, for all practical purposes. When electrical insulation is added to the conductor, thermal insulation is also inherently added. That conductor will not dissipate heat as rapidly to the atmosphere and will become hotter than the uninsulated conductor for the same current. Bundle a bunch of insulated conductors together and stuff them in a conduit, and they will become hotter yet for the same current.

I think you get the picture.

You're looking for ampacity charts.

Try this link:

http://online.physics.uiuc.edu/courses/phys436/spring06/Lecture_Notes/P436_Supp_HO_01/American_Wire_Gauge.pdf

Get a book from a cable manufacturer this will give you max A mV/A/m etc from these fiqures you can calculate cable size for load and distance

you can find a software solution at

http://www.intelisoft.co.uk/