Before “Frozen,” Idina Menzel was merely a Tony-winning Broadway star. After “Frozen,” the singer and actress found herself engulfed in the Disney animated musical’s global blizzard of popularity.

“Frozen” is the highest-grossing animated movie in history. Menzel sings and speaks the role of Princess Elsa, the “Frozen” character who performs the film’s Oscar-winning hit, “Let It Go.”

Menzel recognized the beauty of “Let It Go” when she first heard it.

“But I had no idea that it would become the phenomenon that it’s become,” she said before the start of her 2015 world tour, which comes to the Saenger Theatre in New Orleans on Thursday, July 30. “When a role or a song has such reciprocity, when you’re putting out all of that and you’re getting back so much as well, that’s when you feel truly grateful.”

Despite the international impact of “Frozen” and “Let It Go,” Menzel’s on-stage mission hasn’t changed. She wants audiences to leave feeling as if they know her.

“The thing that I’m most proud of is my ability to give an intimate performance,” she said. “Even though my profile’s gotten bigger because of things like ‘Frozen,’ I’m still able to connect with every person in that audience. That’s challenging to do, the bigger the venues get, but it’s possible. I try to be honest and authentic and stay in the moment.”

Being open to discovery during performances is especially important.

“A lot of times I discover things in front of thousands of people,” Menzel said. “When I was younger, that was frightening; but I learned that the only way to connect with people is to allow yourself to be vulnerable.

“Being a creature of the theater, eight shows a week, I embrace things that keep it fresh. … I want every city, every audience to feel like they got something specific to that evening.”

During her world tour, Menzel sings “Let It Go” as well as material from her two decades of stage work. There are songs from “Rent,” “Wicked” and “If/Then.” There’s an Ethel Merman medley (“There’s No Business Like Show Business,” “Anything Goes,” “Everything’s Coming Up Roses”) and interpretations of songs by Barbra Streisand, The Police and Radiohead.

“Although ‘Let It Go’ is the only ‘hit’ radio song in my career, I consider songs like ‘Defying Gravity’ (‘Wicked’) and songs from ‘Rent’ to be my other hits,” Menzel said. “If the audience can sing every word, that’s my hit song.”

Her international tour — including Korea, Japan, the United Kingdom, the Hollywood Bowl and, in her native Nassau County, New York, the Nikon at Jones Beach Theater — represents childhood dreams fulfilled.

“When I was a kid, I thought I could do anything,” Menzel said. “Now, as a mature woman who’s got the sense knocked into her, I’m ecstatic. Like, ‘Oh, wow. A show at Jones Beach.’ Last year at Radio City (Music Hall), that was another total milestone.”

As much as “Frozen” and “Let It Go” made such high-profile performances possible, Menzel doesn’t feel overwhelmed by the hit song and movie.

“People don’t realize that ever since ‘Rent,’ each defining role I’ve had has garnered a very young audience,” she said. “Between ‘Rent’ and ‘Wicked’ and even ‘Glee’ and now ‘Frozen,’ I’ve always navigated a wide demographic. Which is a very lucky thing, a gift, but it also can be tricky.”

Besides her tour, Menzel has begun the process of making a new album. It’s the follow-up to her 2014 Christmas collection, “Holiday Wishes.”

“I’m putting my heart there and exploring different sounds,” she said. “I’m not limiting myself, I’m just doing what I feel in my heart. And then I’ll see if there’s a theme or trend going on and pick the songs that tell that story.”