I don’t think there’s an answer to the question, really - it depends on usage patterns, mostly, and to some extent on history.
There won’t be any hard limit.
Mostly what you will notice is response times increasing as the number of simultaneous users increases. If you have very peaky traffic - like for live sports events - then you’ll need more resources.
As your forum history gets deeper, with more accumulated posts from more accounts, each database operation will get a bit slower and will need more resources. Similarly if you have very very long threads.
So, how many users active in a week, how many active together in a minute, how many tens of thousands of posts, those are the variables you might look at.
I think there are only a few ways to do this
- spend the maximum amount of money on the best possible machine and hope
- buy a reasonable machine and keep upsizing it whenever it is shown to be too small
- ask people who run similar forums what their forum statistics are and what their systems are like.
Edit: see also this recent technical thread