The formula for calculating cable size for single phase circuits is wire circular mils = (conductor resistivity)(2)(amps)(one way distance in feet) / allowable voltage drop. This formula is based on Ohm's Law.
For three-phase circuits, the formula varies. It is wire circular mils = (conductor resistivity)(2)(amps)(one way distance in feet)(.866) / allowable voltage drop. In standard formulas, the conductor resistivity for copper is 11.2 and for aluminum, it is 17.4 when the temperature is 127 degrees Fahrenheit. The National Electric Code only allows a maximum voltage drop of 3 percent on a main circuit branch, and this should be taken into account when determining cable size.