I don't know that there is a standard dimension. Just wing it. The whole piece should fit between the rails of your bottom board, and under the edge of your hive. Consider making it a tiny bit smaller, because the wood may swell and make it harder to get in and out.
As for the openings, about 3/8" high, and about 1" across for the smallest, and about 3" or 4" across for the medium. If they bees need more room than that, just remove it completely.
Remember, bees are adaptable. They are happy living in a tree, and they only need about 1/4" gap to get into a place.
Why does it have to fit under the edge of the hive body? I make mine taller and the bees figure it out. Its also easier to nail in place when it fits tight against the hive body but does not slip under it. Just a thought.
Also a study was done that indicated leaving entrance reducers in place year round does not result in any less honey. So why remove entrance reducers at all.
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