Depending on how you do the math, Amazon Web Services (AWS) has become, or is on the verge of becoming, the $10 billion business that Amazon CEO Jeff Bezos envisions.

Amid an earnings report today that sent its stock soaring after hours, Amazon reported AWS sales reached $2.6 billion in the first quarter, which ended March 31. That's up from $1.6 billion for the same quarter in 2015.

AWS's profitability climbed as well in the first quarter, with operating income of $604 million, compared with $195 million a year ago.

Bezos's actual statement, in an April 5 letter to shareholders, wasn't really a prediction so much as a simple fact: AWS was easily on pace to become a $10 billion-a-year business. Now that quarterly revenues have exceeded $2.6 billion, that's kind of come true – AWS has reached a $10 billion run rate.

Sales for the past four quarters total only $8.89 billion. But that metric seems likely to crack $10 billion as well, when second-quarter earnings arrive. (My back-of-the-envelope math says it would require second-quarter sales to grow about 38 percent from the previous year's — completely possible, considering AWS grew 64 percent year-over-year in the first quarter.)

Either way, $10 billion isn't much more than a number that's nice and round. Amazon is certainly happy to see AWS bring in $8.89 billion.

As for Amazon itself, the company reported revenues of $29 billion and net income of $513 million, compared with year-ago revenues of $22.7 billion and net losses of $57 million. The figures topped analyst estimates and sent Amazon's stock up 12.6 percent to $677.89 after-hours.