Instagram, an Internet start-up in San Francisco, has no revenue and about a dozen employees. It has not yet celebrated its second birthday. But to Facebook, it is already worth a billion dollars.

Facebook announced on Monday that it would pay that much in cash and stock for Instagram, the latest big winner in an industry that seems to be more awash in money by the day.

Instagram joins other out-of-nowhere Internet hits like Groupon andYouTube. The acquisition, which is Facebook’s largest to date, could give it a stronger position on mobile devices.

Instagram is essentially a social network built around photography, offering mobile apps that let people add quirky effects to their smartphone snapshots and share them with friends.

It has dozens of competitors, but Instagram stands out for its fast ascension and almost cultlike following. It has 30 million users who upload more than five million photos a day, even though it was available for only Apple devices until last week, when the company released an Android app