Convert AWG to Inches
J, 33 26 bytes

0.46%92^39%~*@".{3+".,~1-#


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Takes input as a string with gauges less than zero as a string of zeroes. Finds the index of that string and divides 0.46 (the diameter of 0000) by the 39th root of 92 (the ratio between gauges) that many times.

Explanation

0.46%92^39%~*@".{3+".,~1-#  Input: string S
                         #  Length of S
                       1-   Subtract it from 1
                   ".,~     Eval S and append it, forms [1-len(S), eval(S)]
                 3+         Add 3 to each
            *@".            Sign of the eval
                {           Use that to index into the previous list
        39%~                Divide by 39
     92^                    Raise 92 to that power
0.46%                       Divide 0.46 by that and return