Are you talking about the width across the flats, or the diameter of the spoke? Typically spoke nipple flats are about 1.25mm oee the size or the spoke. So I'd expect a 13g spoke to be about 3.55-3.6mm across the flats. But this is only a rough guide, and there is not any single standard for spoke nipple flats.
It could also be a 12g nipple with deeper cut flats, though this isn't likely.
This is why I have a large collection of spoke wrenches, including a variety of the multi-size round types. When faced with an odd nipple, I start trying them randomly until I get a fit.
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