Yes, if you're soldering the ends together to form a bangle, the thickness (gauge) of the wire does make a difference. You'll need a different length of wire if you're using, say, a 8 gauge wire, than if you're using a skinny 18 gauge wire.
To find out precisely what length you'll need, take the inside diameter you want for the bangle, add the thickness of the wire, and multiply by pi (3.14159265. . . etc.; 3.14 will do fine). For the most precise measurements, use millimetres, rather than imperial measurements.
Thus, for instance, if you were making a fairly sturdy 2.5" bangle out of 8 gauge wire, your measurements would look like this:
63.5 (this is the inside diameter in mm for the bangle) + 3.25 mm (the thickness of 8 gauge wire) = 66.75
Multiply 66.75 by pi (i.e., 3.14; I use an online pi calculator) = 209.7 mm, or about 8.25"
(I'm using the wire thickness measurements for sterling round wire at Rio Grande.)
But if you wanted a much thinner 18 gauge bangle, your measurements would look like this:
63.5 (inside diameter in mm) + .99 mm (thickness of 18 gauge wire) = 64.49
Multiply 64.49 by pi = 202.6 mm or a little less than 8"
Remember that those measurements are based on the finished length of the wire, so if you're likely to be filing off much to get the ends flat enough to solder tightly, you'll need to account for that.
