Cross Section and the Maximum Current

Where I is current in the conductor, J is the current density, and A is the cross-sectional area. The dot product of the two vector quantities (A and J) is a scalar that represents the electric current.

There are other factors besides conductor area that apply.

Virtually every wire/cable manufacturer has tables that give the capacity of their conductors, taking into account the type of insulation, location of the conductors, and the nearness of conductors to each other.

Virtually every electrical code has similar provisions that pertain to this.

There are gazillions of threads already on CR4 that address this topic.

This table is just an example but to design a cable size you have to consider the following factors.

1- Derating factor for ambient temperature

2- Derating factor for maximum allowable conductor temperature

3- Derating factor for underground soil thermal resistance

4- Derating factor for cable grouping

5- Derating factor for A/G tray covers

6- Derating factor for A/G tray maintained spacing

7- Cumulative effect factor for A/G trays

8- Derating factor for A/G conduit (NEC and diversity factor)

9- Derating factor for A/G fire coating

10- Derating factor for A/G fire stop

11- Derating factor for A/G fire wrap

There are plenty of tables like that one in British Standard 7671.