[hytham1989]

I want detailed explaining with equation equations

[Stratmando]

Usually goes by Wire Gauge, not diameter.
Basically you Start with your load and see what it needs, then you size the wire accordingly and a breaker to protect the wire from burning.
#14 for 15 Amps
#12 for 20 Amps
#10 for 30 Amps
#8 For 40 Amps and so on, and is called Ampacity.
Wire size may need to be increased due to voltage drop if it is a long run, insulation is another factor.
There are Exceptions as well.

[sinnadurai]

Diameter doesn't decide the current rating but the cross section and composition of wire whether stranded,single,flexible as well as its insulation,ambient temperature etc