Operating income for the cloud division rose to $391 million from $77 million. No wonder analysts on a conference call with Amazon financial executives offered their congratulations.

Even before the after-hours surge, Amazon shares were up 55 percent this year. Analysts have been rushing to upgrade their already enthusiastic ratings.

There seem to be only a few skeptics left.

“This market is just nuts,” said Sucharita Mulpuru, an analyst with Forrester Research. “Amazon’s profit is effectively 0 percent of revenue and everyone cheers. Apple grows faster and has a profit that is 20 percent of revenue, and the stock tanks. Amazon’s stock price doesn’t seem to be correlated to its actual experience in any way.”

Amazon hired another 50,000 employees over the last year, increasing its head count by 38 percent. Many of those workers are in its network of more than 100 fulfillment centers.

Amazon, which tends to be conservative in its forecasts, said it may once again lose money in the third quarter. It could lose as much as $480 million or make as much as $70 million, it said on Thursday. Last year, it lost $544 million in the third quarter.

Behind all the excitement is the same story that has powered Amazon from the beginning: It is the leading e-commerce company, and e-commerce is going to be really big. Amazon’s dominant position, its admirers believe, will allow it to undercut competition and bring home large profits. In the most extreme case, it will control the delivery pipeline of goods into homes, kind of the way cable companies once controlled the flow of entertainment.

“Walmart has been the de facto retail king for the last 20 years,” said Mr. Moser, the Motley Fool analyst. “They were very good at bringing the consumer to the store. But technology changes so fast. What Amazon is doing is building a company focused on bringing the store to the consumer.”