How do you calculate what wire thickness you need for a given voltage?

Answer 1

The cross sectional area of the wire is determined by the current (amperes) flowing through the conductor. There are also a few environmental attributes that affect the heat dissipation. Open air, in duct, direct buried, etc.

The voltage level will affect the insulation type and thickness. This higher the voltage, the greater the insulation.

Answer 2

actually it's not the voltage you need to worry about - the thickness of wire is determined by the maximum amount of current you intend to draw through it