Shailene Woodley has gone from impressive newcomer to star at rocket-sled speed.

She earned rave reviews for her film debut at 15 as George Clooney’s bad-tempered daughter in “The Descendants.” She won an acting prize at Sundance for her turn as a touchingly vulnerable smart girl in the indie hit “The Spectacular Now.” She took the reins of a high-profile Hollywood franchise in “Divergent,” based on the hit series of dystopian young-adult books by Veronica Roth.

Her next project, opening today, puts the full weight of a serious studio film on her shoulders. She stars as Hazel, a teen with cancer who experiences first love with a similarly ill boy in the adaptation of John Green’s bestseller “The Fault in Our Stars.”

Against all odds, the 22-year-old Californian seems to be keeping her head on straight. Her recent appearance on David Letterman’s show became an extended teasing session as he grilled her about her high regard for organic living and herbalism, which includes eating clay. “Haven’t you heard of Metamucil?” he asked. Blogs have poked fun at her wearing Vibram FiveFinger shoes to the Golden Globes, and setting the mood every morning by screaming “Exciting day! Exciting day!” Miles Teller, her co-star in “The Spectacular Now” and “Divergent,” has told interviewers he’s “pretty sure she lives in a tree.”

While she’s acquired the image of being America’s Favorite Moonbeam, Woodley has remained authentic and serenely good-humored through it all.

“I don’t say the things I say for others, I say them because it’s my truth,” she said recently by phone from New York City. “I try to live by two things. A, it’s none of my business what other people think about me. And B, you do you, I’m gonna do me, each and every day.

It probably helps her grounded disposition and her acting that both her parents are psychologists, she said.

“Growing up it was always, ‘How does this make you feel? If this person hurt your feelings, why were your feelings hurt?’ It helped me observe people, like to figure out what made them so sensitive to something that was said. What is the rhythm of their mind in getting offended by this or excited by this? Empathy and compassion were two things that were hard-core ingrained” in the household, she said.

That’s one reason she’s proud, amid all the summer blockbutsters, to be in a film about recognizable humans.

“Even though there’s no superpowers and whatnot, the truth of what these people are going through is so relatable.”

Woodlley plays Hazel, a bright girl who dislikes being reduced to a cancer diagnosis but withholds herself emotionally for fear of the pain her eventual death will cause.

“Not everyone can relate to the cancer, but we all know the feelings of being in love, being sad, grieving and being happy, celebrating life.

“It’s not about cancer. It’s about first love and loss. It’s about appreciating moments and not taking things too seriously because nothing is guaranteed in life. When there’s a finite time line on your life, you’re not worrying or stressing or feeling guilty about the small things in life that most people in the world are wasting their time on.”

To portray a character with a terminal illness honestly, she said, “you pretend to be a normal human. Cancer doesn’t define a person. For Hazel, I didn’t think ‘I’m playing a girl with cancer.’ I thought, ‘Omigod, I’m playing a girl who’s falling in love for the first time.’ “

So does she live in a tree?

“Um, no. But the place that I used to live in had a tree growing through it. I don’t know if that constitutes a yes. I guess that’s a yes-and-a-half.”