The old truth was that you should have 1-2" clearance between your crotch and the top tube, but current designs often use sloping top tubes whch messes up the old reference. There are plenty of sites that'll give you some guidelines, do a search for "bike fitting" and see what you'll come up with. Try a couple of the different methods and them pick a comparison from the middle of the group. The most crucial value is that when you're in the saddle you should be able to have your leg almost fully extended when the pedal is at its lowest position.
The best bike to buy for a nine year old active boy is a 24in-wheel bike with a 3-speed hub gear.
For a 13 year old it depends on your size and your experience with dirt bikes, but an 85 is usually the best size bike and fastest for a 13 year old. Unless you are really tall which you would need a 125.
A very small bike
The bike that you should buy for your nine year old son is that with a 20-inch wheel with suspension forks and adequate front suspension.
The recommended girls bike size for a 10-year-old is typically a 24-inch wheel diameter.
If that is the correct size for her feet then that is fine.
It all depends on how big he is. If he is small for his age he will need a smaller bike or if he is big a larger one. Best thing to do is ask the attendent at the bike shop.
The recommended bike size for a 7-year-old child is typically a 20-inch wheel diameter.
For a 6-year-old, you should consider getting a bike with a wheel size of 16 inches. This size is typically suitable for children around that age and height.
The recommended boys bike size for a 10-year-old child is typically a 24-inch wheel diameter.
For a 12-year-old, a bike with a wheel size of 24 inches is typically recommended. This size is suitable for most children in this age group and provides a comfortable and safe riding experience.
The appropriate bike size for a 12-year-old is typically determined by their height. A 12-year-old child with an average height of around 4 feet 11 inches would generally require a bike with a wheel size of 24 inches. It is important to ensure that the child can comfortably reach the handlebars and pedals while sitting on the bike.