In the NFL, after a touchdown the ball is placed on the two yard line. In college, the ball is placed at the three yard line. So it's a 19 yard kick in the NFL, 20 yard kick in College.
10 yards for the length of the endzone + 7 yards that the kicker and holder are set up behind the line of scrimmage + 2 yards, for the ball being placed on the 2 yard line(or 3 for college.
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After a touchdown in the NFL the ball is placed at the two yard line for the conversion. Generally, when teams make a place kick, the holder kneels down 7 yards behind the line of scrimmage. That would mean the ball would be held for the kicker about 19 yards from the goal posts.
One point. The team also has an option to do a play after they score a touchdown, which is called a two point conversion. In this the team can run one pay in an effort to score two points instead of one point by kicking it through the uprights (the yellow poles in the endzone).
So yes,
Kick after touchdown, One point
Two point conversion, Two points