Determining "Critical Mass" for a Web Application

I'm in the process of building a web application that will need a healthy user base from day one to be successful (similar to a stackexchange site).

I'm already taking signups but I'm curious how many active users would be needed to sustain the site initially (X ) and as a result how many signups I should gather (Y ) before "unleashing" the site. (since not every user that signs up for info will register on the site and become an active user).

Note: even when I do "unleash" it I expect the first bit will be a closed beta (e.g. Trying to harness some "exclusivity" power) enable tweaks, and further drive interest for new users to sign up.

A few notes:

1. The site will be free so there will be no financial barrier to entry.
2. The target market is global, (e.g. Every time zone) and for anyone from age 13-90+

Does anyone have any stats on % of conversions of "signed up for info" (X ) vs. "registered as a user"?

I tried to work this backwards randomly guessing that 50 users a day would likely be enough to keep it afloat... and that I'd (again randomly guessing) that users might visit 1-2 times a week (~350 users needed)... and that hopefully 30% of those that sign up for info actually visit and try out the site... thus obtaining ~1,200 interested users up front would be needed... but I have no idea how wild/realistic any of these numbers/percentages are.

You will have a very hard time reaching critical mass through subscriptions, unless your product is a cure for cancer.

Real world numbers are a lot worse than your calculations. Based on Mailchimp newsletter statistics, 30% is the group that will at least open your beta invite email. Others won't even do that. Typically not more than 40% out of that 30% are the ones who get as far as clicking the invite link. A lot of them will close the tab without registering. And most of the registered users will never come back to the site. I would be surprised if you could convert your subscribers into active users by a rate bigger than 5%, especially if your service is useless without critical mass.

You have a chicken and egg problem here. This is why it's a good idea to design a service in such a way, that even though the social part has real added value, the service is useful even for the first lonely user.

If that's not possible, you'll have to think of partnerships, to inject somebody else's userbase into your service all at once. I don't think just waiting for subscribers to pile up will do it.