SAN FRANCISCO — Netflix’s second-quarter earnings more than doubled as new episodes from a hit series helped the Internet video service surpass 50 million worldwide subscribers for the first time.

The gains announced Monday include an additional 570,000 U.S. subscribers, slightly more than Netflix’s management predicted. The quarter is typically the company’s slowest of the year, as people spend more time outdoors instead of watching video.

Investors applauded the second-quarter results, pushing Netflix’s stock up $4.05 to $456 in extended trading. The shares have surged by 23 percent this year, while the Standard & Poor’s 500 index has increased 7 percent.

The second quarter featured one of Netflix’s marquee attractions, “Orange Is The New Black,” which returned for its second season in early June. As with Netflix’s other original series, all 13 episodes of “Orange Is The New Black,” were released simultaneously so subscribers could watch the story unfold at their leisure.

“Consumers are enjoying more than ever being in control of their own schedules, able to click and watch whenever they want,” Netflix CEO Reed Hastings said in a Monday interview.

Without breaking down the specific viewership numbers, Hastings said “Orange Is The New Black” became Netflix’s most-watched series during the first month after the June 6 release of the second season.

“Orange Is the New Black,” set in a women’s prison, received 12 of the 31 Emmy Award nominations bestowed upon Netflix programming for this year’s awards. Netflix’s Emmy nominations eclipsed the 24 garnered by longtime pay-TV channel Showtime, which collected 24, but lagged far behind HBO’s pace-setting 99 nominations.

Netflix ended June with 36.2 million subscribers in the U.S. and another 13.8 million customers in roughly 40 other countries. The Los Gatos, California, company picked up 1.1 million subscribers outside the U.S. in the second quarter, a figure that also topped management’s projections.

The company said it expects to add another 3.7 million subscribers worldwide in the current quarter ending in September, including 1.3 million U.S. customers. It also plans to start selling its Internet video service in six more European countries in September, including Germany and France. Netflix’s long-term goal is to reach as many as 90 million U.S. subscribers and more than 100 million internationally.

The second-quarter performance will likely alleviate any concerns that a price increase imposed in early May would undercut Netflix’s growth. Netflix raised its rates by $1 to $9 per month for Internet video streaming in the U.S., but the company eased the blow by allowing existing subscribers to continue paying the old price for at least two years.

As Netflix’s video-streaming service steadily grows, the DVD-by-mail rental business that once was the company’s foundation is slowly crumbling. The DVD rental service shed another 391,000 subscribers in the second quarter to end June with fewer than 6.3 million customers. That’s a decline of 55 percent in less than three years.