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1/4" is 23 gauge. 1/2" is 19 gauge... It's thicker.
The gauge is the thickness of wire used. For instance, your standard chain link fencing is 9 gauge.
Use this info as you wish, 1/4" didn't stop a coon from taking one of my pullets. This was brand new 23 gauge on a new run. Pulled the welds apart in the center. I only use 1/2" or thicker wire now. I don't trust 1/4 " much more than standard chicken wire. It's possible it could have been a bad...