Is it too late to start ballet at 15, almost 16?

Recreational ballet is for anyone of any age. Find a teen beginner or teen/adult beginner ballet class and get started. There is no need for private lessons. They are very expensive and are better suited for a dancer who is more advanced and who has a specific issue that need addressing. Basic ballet is better learned in a group setting.
You don't need to do anything, however, you could take some pilates or yoga. Pilates is how professional dancers cross train. It elongates the muscles, builds core strength and flexibility. It will help get your body ready to accept ballet training.
For inspiration, here is a clip of Vanessa Sah (Anaheim Ballet school,) who started ballet at age 19. While only a recreational ballet dancer, it shows that a lot can be accomplished if you put in the work and have a few of the required gifts for ballet.
http://www.youtube.com/watch?v=Z0xjoPIZem0

It's never too late to start anything. I started dancing in April this year and I'm 19 ;3 follow your dreams and do what you want! It's never too late ;D

Yes! Definitely. Its never too late. If I were you I would ask your dance teacher if she, or an older student, could meet with you privately for lessons since you're just now starting. The sooner you start, the sooner you'll be up on pointe. :)

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