To be dead sure, take a caliper or mic to the hardware and measure the rod. Just be sure it is .010 less than nominal groove diameter or smaller.
But here are a few numbers for the rod sizes that are commonly available.
7/16 inch diameter is .437, which is ideal for 45 cal.
3/8 inch diameter is .375 which will work well for calibers over 375 but not 375
5/16 inch diameter is .312 so it will work well for 8MM or .321 & .323 nominal and larger calibers.
1/4 inch diameter is .250, which gets the nod for .270 up to and including the 30 calibers.
3/16 inch diameter is .187 and is suited to 22 cal, 6MM etc
If the rod is quite loose in the bore, I normally hold it in my hand and using a light weight hammer, like an 8 oz, tap it sharply on the end until a rivet head forms. Pean it until it fits the barrel fairly close. Do this with the full 36 inch length if you buy from a hardware, so the inertia is highest. Then trim till the rod extends only about 2 inches out of the longest barrel you will use it in, when setting on your lead plug which will be swaged. If desired you can wrap enough electric tape every 4 inches up the rod, to make it fit close, and make you feel comfortable about beating on it inside the barrel. But mild steel rod is softer than any centerfire barrel and will not damage it if unprotected. Don't use brass rod. It will work hardend and can damage a barrel
