There is some similarity between the different standards at certain aperture sizes, but no real easy conversion factor for moving between them. Conversion charts are usually the best option, like the one included in the appendices of Kelly and Spottiswood's "Introduction to Mineral Processing" which I've always used.

The problem stems from the fact that screens were originally sized on the basis of the number of holes per square inch, since this was the easiest thing to measure/control, but different manufacturers/standards used different thicknesses of wire. So a #10 mesh Tyler screen (10 holes per inch) equates to a 1.7mm aperture under the ASTM standard, 1.68mm (but also #10 mesh) under the B.S.S and 1.6mm under the French and German standards. However, a #16 mesh Tyler screen equates to 1.0mm under all of those standards. These days of course the most popular system is to just use the aperture size in microns or millimetres, since it eliminates a lot of the confusion.

Oh, and in case you're wondering - the gap between screen sizes was originally based on a square root of 2 series, since this meant the area of aperture doubled with each successive screen. Of course since then intermediated screens have been added, usually based on a fourth root of 2, or tenth root of 10, but the sizes certainly aren't just picked at random.