For wire conductor size we have AWG (which is American Wiring Guide) and metric standarts (SI). For cable size you need to have a look at the cable manufacturers’ catalogues.

Here you may have the table for conversion between these tables;

AWG	SI ($latex mm^2$)
6⁄0	170.30
5⁄0	135.10
4⁄0	107
3⁄0	85.0
2⁄0	67.4
1⁄0	53.5
1	42.4
2	33.6
3	26.7
4	21.1
5	16.8
6	13.3
7	10.5
8	8.36
9	6.63
10	5.26
11	4.17
12	3.31
13	2.62
14	2.08
15	1.65
16	1.31
17	1.04
18	0.823
19	0.653
20	0.518
21	0.410
22	0.326
23	0.258
24	0.205
25	0.162
26	0.129
27	0.102
28	0.0810
29	0.0642
30	0.0509
31	0.0404
32	0.0320
33	0.0254
34	0.0201
35	0.0160
36	0.0127
37	0.0100
38	0.00797
39	0.00632
40	0.00501

And from $latex mm^2 $ to AWG we don’t have a directly conversion since AWG don’t have something like 30.5 or 10.2, but we can estimate how near they are to each other for example taking AWG20 as 0.5 $latex mm^2 $ does not seem wrong. According to those estimations we can have a chart like this;

SI ($latex mm^2$)	AWG	DEVIATION ($latex mm^2$)	DEVIATION (%)
0,5	20	+0,018	3,6
0,75	18	+0,073	9,73
1	17	+0,04	4
1,5	15	+0,15	1 0
2,5	13	+0,12	4,8
4	11	+0,17	4,25
6	9	+0,63	10,5
10	7	+0,5	5
16	5	+0,8	5
25	3	+1,7	6,8
35*	2	–1,4*	4*
50	1⁄0	+3,5	7
70*	2⁄0	-2,6*	3,71*
95	$latex \frac {4}{0}$	+12	11

$latex *$ These ones may be a little smaller size or deviation from the original size may be higher so be careful while choosing these ones. These are not direct or near conversions.