He was just a child when he joined Fairy Tail. When did Igneel decide to train Natsu and for how long?
We are shown both his appearance with Erza, Grey and Lisanna as children so it can't be very long that he trains under igneel. His appearance with igneel and with the group are very close, if I remember, practically the same.
At a maximum, I would suggest 3 years but I don't think it would be less than a single year. It's theorized that Natsu was around 8-9 and then Natsu was 11-12 when he joined Fairy Tail.
We don't know for sure though
We are never told Natsu's biological age and even if we were it would never make sense:
- First generation dragon slayers do not age past adulthood and it is doubtful the stopping of aging happens all at once. (Acnologia is very young)
- He has time traveled, been in suspended animation and even dead for awhile. Time is probably very fluid from his perspective.
- He is even less human than the other dragon slayers so maybe he did not age properly(its suggested he was weaker than Gray as a kid but slightly stronger in his teens IE his power doesn't grow at the same rate as others).
For these reasons guessing his actual biological age is a shot in the dark(early dawn at best but VERY early). Yes, it is probably 16-21 but that is a wide range and could still be wrong for the reasons above. We do not know and unless a character/writer strait up says it (which seems unlikely) we are not going to be able to figure it out.
Don’t forget that in the beginning of fairytail dragon cry Natsu looks about 4 and is shown with igneel in a cave though I’m not sure of this is how they met or not. Then further on it shows Natsu looking about 11 or 12 in the rain staring at the ground sometime after igneel left. And that is when he meets gramps and later joins fairy tail.