Can measure for you tomorrow, but in general it is a perfect circle plug that is at most 1/4" past where the prongs all are. It does then extend out about 2-3 inches front the plug with that same thickness before it changes into a cord - i.e. the adapter part. I'd say off hand you need a good 4-5 inches clearance away from the plug before the cord can twist to a direction...
If all that makes sense, will add a couple pics for you if helps. (edit: oops for some reason it added them multiple times!)
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