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Instagram rocketed to 30 million iOS users in 18 months and was named iPhone app of the year in 2011. It is one of the best apps for taking and sharing photos from the iPhone. Its square images and assorted image filters let anyone make retro, techno and pretty pictures out of mundane shots of their kids, pets, food. Instagram’s Android version, released last week, got millions of downloads immediately. But $1 billion, if true, is still a crazy number. Instagram doesn’t make any money. Nor did it say it was focusing on revenue. It is still chasing big users. Kevin Systrom, Instagram’s CEO, wrote this to calm down his users in response to the deal. An excerpt:

It’s important to be clear that Instagram is not going away. We’ll be working with Facebook to evolve Instagram and build the network. We’ll continue to add new features to the product and find new ways to create a better mobile photos experience.

It’s not clear what the Facebook deal means for the Series B funding round that may have closed last week, led by Sequoia Capital, Thrive, Benchmark and Greylock at a reported $500 million valuation. But the fact that Facebook would pay 2x what the company was supposedly worth within a week’s time suggests this is a defensive move. Facebook has the money (almost $4 billion in cash on hand as of December 2011), and certainly isn’t desperate for more users, most if not all of whom are already on Facebook (which greatly influences the price-per-new-active-user Facebook is paying. See crude math below.)

Fred Wilson has said that Facebook is really about photos and this only underscores that. The mobile-social photo sector is still amorphously led but if anyone is harmed by this deal it is Yahoo. Facebook is really going after its Flickr property here, to put the nail further in Yahoo’s coffin. (To its discredit, Yahoo hasn’t done anything with Flickr lately). Zuckerberg is playing chess, making a defining move in how it stands in the photo space. It’s like what Google did with YouTube.

One problem this will solve for Instagram’s 30-something million users is that sharing an Instagram photo on Facebook from your phone pretty much sucks right now. Here comes the much needed integration: bigger photos, more detailed info about the filters, etc. Right now all you get when you post an Instagram photo on Facebook from your phone is a small link and a thumbnail image. A better integration will stimulate more sharing through Instagram.

But a $1 billion for 30 million users that pay nothing for the service? Sounds crazy but consider this: Instagram is getting bought for $33 per user. Facebook is supposedly trading with a market cap of close to $100 billion and has 850 million users, giving it a value of $117 per user. So it looks like a decent bit of funny-money arbitrage, using well-endowed Facebook shares to acquire users and solidify hold of a strategic asset at a lower valuation. We don’t yet know how much of the deal is in cash vs. stock, so this calculation could be less favorable sounding but it still makes sense with Facebook currency.

Here’s a video Forbes editor Michael Noer did with Instagram CEO Kevin Systrom for our 30 Under 30 special. According to Wired’s Mike Isaac, Systrom netted $400 million from the sale.