I'm 12 and I started BJJ 2 months ago, and I've been wondering if by the time I'm 18 will I still be in the kids category of belts? According to my math, a yellow belt?
I talk about this in more detail in my answer here:
The answer is that most BJJ schools will automatically convert (without need for a test) your children's rank into an adult rank when you reach 16 years old.
But as my answer in the link above suggests, the adult rank you actually receive may depend on other factors besides what children's rank you had. Your instructor may add or subtract a grade or two. So nothing is entirely certain.
This may also depend on your particular school, if they have a policy of only considering 18 years old and above as adults. I think it's usually 16 years old, not 18.
You should ask your instructor this question if you want to know your particular school's policy.
Hope that helps!
From a Judo perspective, the answer is "it depends". The yellow belt is next to the white belt, so it's very probable you could achieve the yellow belt in a short period of time, if and only if you practice and learn the basics of the sport in the short period of time. It all depends the amount of time you dedicate to the practice. A recommended amount of time for somebody that practices Judo as recreational sport is 2 or 3 times a week. Also, your sensei makes the ultimate decision whether you progress from one belt to the next.
I used to practice in Chile, where if you practice 2 or 3 times a week and compete in some tournaments in a year, the average time to progress between grades was 1 or 2 years per belt, so from white to yellow it could take you at least 1 year. But if you barely train, don't expect to be yellow in the short term.
In summary, if you are 12 and you train 2 or 3 times a week, it is very possible that at 13 or almost 14 years old, you will be a yellow belt.
Anyway, the belt is only to hold your judogi closed. The important thing is the path, the things that you learn, not the color of your belt.