Good question and great answers so far. I have no real answer other then to "confirm" some of the given answers with my experience.
I can handle the American bombshell small shellshock which is 3.1 inch diameter or 9.6 inch circumference all the way from top to bottom the same size.
I can handle the American bombshell bunker buster which is 3.2 inch diameter or 9.8 inch circumference at the widest top edge, and 2.9 inch diameter or 9.1 inch at the shaft.
These are soft material. I also have a normal shaped butt plug with a 2.9 inch diameter or 9.1 inch circumference. This one is half way between soft and hard.
The toys mentioned will fit great and are inserted easily, when my butt is gradually opened up first with a smaller toy and with using lube.
Now I do have the Ace of Spades which is 3.1 inch diameter or 9.6 inch in circumference. This one is made from a hard material and for the love of it I can not get this one in, tried different angles and positions, being as horny and lubed up as I can, being warmed up (toys and room temperature), but nope... I can't get it in yet.
So I can only confirm that the hardness of the material, and perhaps it shape play a big part here.