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A fixed-choke Remington shotgun barrel SHOULD have it marked on the left side of the barrel. Barrels which use choke tubes will obviously not have a marking.
There's an old rule of thumb on full-choked 12 gauge barrels that a dime won't fit down the end of the barrel. Beyond that, the opening becomes larger.
If you do a Google search on "shotgun choke dimensions" you'll get a lot of links to websites which list the various dimensions and will give you a lot of reading material.
Here are a couple of examples:
http://www.colonialarms.com/pdf-files/page7.pdf
http://www.hallowellco.com/choke_chart.htm
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Choke dimensions
Re: Choke dimensions
Look here. Everything you always wanted to know.
http://www.briley.com/
http://www.briley.com/
What could have happened... did.