The US insignia is not measured and sized according to the diameter of the circle. That would work for two of the six on the photo, but not the other four.
The diameter of a US insignia is the circle made by connecting the tips of the stars, so for the two on the upper right, your method is correct,,,,,Full Size is found by just measuring the circle and mulitplying by 48.
For the other four, you measure the diameter of the "main blue part" of the circle, leaving out the Red, Yellow or Blue surrounds that were added after the specs were finalized.
Since you got 39" as your answer, it seems that you measured the full diameter of one of the "bad choices" instead of the "diameter at the star tips"
I hope this helps point out why we can't just measure and multiply everything, we have to do it the same way they were drawn out in the first place. (If we plan to match the names up, that is)
This might even help someone save some money, because if you know the diameters you want in your scale, a cheap decal sheet that has small 1/32 or large 1/72 insignia on it may have portions that work on your 1/48 stuff.
Rex