[WMichelsen]

Edited for better clarification:
The carriage bolt is a 1/4"-20 x 1/2" long
- That's 1/4" diameter. 20 thread-per-inch 1/2" in length. That's how it's referenced if you go to HW store.
The barrel nut is 1/4"-20 x 3/4" long
- Again 1/4"-20 to match the bolt, and 3/4" in length
That's what I had on hand, and it worked well.

You could use 3/4" long bolt and nut if you wanted to. There is enough room.
Likewise, you could use 1/2" long bolt and nut. There's enough for the spring to catch onto. But, doesn't feel as secure to me.