I found many online calculators or tables which can give maximum current for the wire. Like 1 mm diameter can handle up to 10 Amperes, 2 mm diameter wire can handle up to 30 Amperes, etc.
Is there any practical equation (formula) for this which will work in a wide range of currents $10^{-3}-10^2$ Amperes (1 milliampere - 100 Amperes) and 0.01-100 mm wire diameter?
Is it linear? If yes, I can make up the formula from all these tables.
I need a simplified case, like a single bare copper cylindrical (round) wire without insulation, in the air with 20-25 Celcius room temperature, etc.
It does not matter for me if the formula will be depending on wire diameter or wire area. I can change it if needed.
UPDATE 1
I tried the answer from Peter Green $$I=15.774 A^{0.6077}$$
and I got this graph
The horizontal axis is wire cross-section (A) in $mm^2$ and vertical axis is current in Amperes. Orange is a calculated graph. Blue is from one of the tables from the internet, here for example https://www.powerstream.com/Wire_Size.htm.
As I see the shape is matching, but values are not. For the current less than 10A, the calculated value is higher, for current less than 10A, calculated value is smaller.
If I put it like this $$I=22 A^{0.6077}$$ then it works much better for the current more than 15A, but still not very good for small currents.
Looks like using these tables is the only way :( I will try to get an equation from the table with the assumptions that true equations should be
$$I=y A^{x}$$
I will try to find y and x and post it here if I will be successful.