That is a 73% jump from the initial asking price of $26 a share, and it means the company is now valued at a little over $31 billion.
More than 13 million shares were traded once they became available an hour after the stock exchange opened.
It is the biggest technology listing since Facebook in 2012.
Twitter floated on the NYSE and not, as some initially expected, the technology-rich Nasdaq exchange, where the likes of Facebook are listed.
It was a big win for the NYSE, which decorated its exterior with banners promoting the offering on Thursday.
Twitter has more than 230 million users, but is yet to make a profit.
Shares in newly-listed companies are often volatile on their first day of trading.
Within minutes, Twitter’s stock price soared more than 80% before falling below its opening price by midday.
When Facebook launched on Nasdaq, its shares were priced initially at $38 each. The stock soared within hours of its debut to a high of $45. But its price later slumped.
It only recovered those losses by September 11, 2013, when shares again touched $45.
Its initial public offering (IPO) was also marred by technological glitches and delays.
To prevent Twitter’s stock sale from having a similar fate, the NYSE ran tests on October 26 using larger-than-normal share volumes.
Twitter is selling 70 million shares, which will raise more than $1.82 billion.
The company, which invites users to send tweets in 140 characters or less, has 232 million active users. According to its IPO documents, these users send 500 million tweets a day.
Twitter’s financials have been under greater scrutiny since it announced its plan to float, especially given that the company is still loss-making.
It lost $69 million in the first six months of 2013, on revenues of $254 million. About 85% of revenues come from advertising on its site, and more than 75% of Twitter users access the site from their mobile phone.
Mary Jo White, head of US regulator the Securities and Exchange Commission, recently warned investors to be cautious of the metrics used by technology companies like Twitter, nothing that investors have become overwhelmed by the sheer magnitude of data.
“In the absence of a clear description, it can be hard not to think that these big numbers will inevitably translate into big profits for the company,” Mary Jo White said in a speech.
“But the connection may not necessarily be there.”
Twitter’s founders saw their paper wealth soar to $4 billion in the wake of the stock surge early this morning, although boss Dick Costolo said that none of the founders would immediately be selling their shares.
The company’s co-founder Evan Williams has a 10% stake in Twitter, making him its biggest shareholder. That stake is now worth a little over $2 billion.
Jack Dorsey, another co-founder, also stands to make a fortune from the IPO. His 4% stake is worth more than a billion dollars.
Another co-founder, Biz Stone, is thought to have made millions of dollars by selling share stakes over the last few years.
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