It mainly depends on the state; each state has its own laws that declare when a child is considered an adult. The typical age is 18 years old for many states also in those laws, it might allow a minor to petition the court to be declared a legal adult, and if allowed by the court, then he becomes an adult. For more information you can visit en.wikipedia.org/wiki/Minor_(law).
18 and up is an age where a man can be matured enough to understand things about life, but others mature too soon and that depends on his or her experiences in life. but 13 below i believe cannot be matured enough to be on their own because they still need guidance.
I'd say 18…you are still growing before that point, both intellectually and physically. Some people say that you're a young adult once your 12 or so, but really that stage doesn't happen until you're at least 20-ish. So if you are still at any age from 0-20, i'd consider you a child.