Formula for Cable Size and Rating Calculation

BS 7671

Yep. It's all in there. GA.

I don't think there is any such thing as "the exact equation" for this. As a practical matter, conductor ampacity is determined by looking it up in electrical-code or manufacturers' tables, with various corrections applied for ambient temperature, conductor configuration, etc.

http://www.energy-solutions.co.uk/cable_conductor.html

Check this chart. Be Sure to apply all applicable code derating requirements

This looks like homework. Laaazzzy, laaaazzzzy homework.

See the numerous previous threads on CR4 covering this commonly asked (homework) question.

use it

1) There are no thumb rules for calculating cable ampacities. Because, the cable impedance variation is not "linear"; only the resistance will vary linearly with respect to the cable size, whereas the reactances (both capacitive and inductive) are not linear with respect to the cable cross section. That makes it difficult to arrive at a formula for calculating the cable ampacity vis-a-vis its size.

Easier method would be to follow the cable manufacturers' catalogues and rating tables (and, don't forget to apply appropriate rating factors).

2) For carrying 100 Amps current, under Indian Industrial Installation Conditions, I would normally go for a 70 sq.mm Aluminium Conductor Cable.