I have a Campagnolo Chorus 9-speed rear derailleur. I am trying to determine the largest cassette I can use. The main question I have is how do I determine what size cage I have. It is not a new derailleur. I have 50-36 chain rings and currently a 23-11 cassette. Would like to go a little bigger on the largest cassette cog if possible.
There are two parts to this - the cage length is the distance between the two jockey gears in the rear derailleur, and this limits how many links of chain it can take up while maintaining tension. Longer cages (like MTB ones) could do 11-42 so a difference of 31 half-links.
Road bikes tend to be narrower, so a short cage might only take up 11-2x. There are many in-between lengths.
So change to the bottom gear, and look to see if your lower jockey wheel could move further forward. Then consider if the chain was a couple links longer and you're in a small/small combo, would the chain touch itself?
The second part of your question is whether there is space for a larger big cog on the back.
The eyeball technique would be to put the bike into its bottom gear, so 36/23. Then look to see how much space is left between the top jockey wheel and the largest cog. If the bike came with 23, then 25 is likely to work, and you might be able to get up to a 28 in there.
Otherwise you have to change the rear derailleur too, which is another cost.