There are some penalties that are assessed at the end of a play. (Don’t ask me what they are, because I don’t know.) So let’s say there’s a play where the offensive team makes 20 yards, and then they’re given 10 yards because of something the defensive team did. So they’ve gained 30 yards on the play, right?
OK, suppose they offensive team is awarded 5 yards (to be added to the end of the play), and they’re three yards to the goal. What happens?
Half the distance to the goal.
Her name was Rio and it’s half the distance to the goal
once
in 1963
for 20 minutes
A penalty is typically(*) assessed after the end of the play if the penalty occurred after the play was over. Say the defensive player plows into the runner after the runner has gone out of bounds, or if player A punches player B after the receiver has been tackled.
(*) I’m going to say “typically” because I just know that folks are going to mention situations where this is not the case. 
Half the distance works in reverse, too.
(Offense on own 10 yd line, holding penalty [normally 10 yrds], ball now on own 5)
And yeah, certain other rules may change things, like holding in your own end zone is a safety. but knowing the half the distance rule will keep you informed enough.
Some diffs between NCAA and NFL in penalties, too.
And never trust the color commentator’s first reaction. Most of them are wrong. Then the research people send them quick info or stats and the color guy acts like it’s what he said all along. Sometimes, I actually miss Howard Cosell.
And sure enough…
On kickoffs and punts, certain live-ball penalties by the kicking team can result in yardage tacked on to the resulting play or marked off and the down is re-played, at the discretion of the receiving team’s head coach.
There’s also certain “spot of the foul” penalties, such as pass interference. Those don’t have a specific yardage penalty. The ball just gets placed wherever the foul occurred.
And for whatever reason, no one answered this. The answer is “yes”.
Sevenwood answered that, and the answer isn’t usually “yes.” If the defense committed the foul during the course of the play, the offense can choose between the yards gained from the penalty (typically 5, 10, or 15 yards) or the result of the play. In the example from the OP, the offense would almost always decline the penalty (5, 10, or 15 yards, depending on the infraction) and take the 20 yard gain instead.
The only time the offense gets the result of the play plus the penalty yardage is when the foul occurred after play was stopped - a late hit or a hit out of bounds, for example.
Maybe I misinterpreted the question. Lemme clarify:
OP, if you stipulate a play where the offensive team makes 20 yards, and then they’re given 10 yards, then yes, it’s does total to 30. However, as has been pointed out, most penalties are not “and then”. They’re usually “take the play or penalty” variety.
Yes, I know that most are the ‘play or penalty’ kind. Since the ‘add it to the end’ kind seem pretty infrequent, I was curious about what happens when the penalty is greater than the distance to the goal. The ‘Right?’ in my OP was in case I was wrong about yardage being added to the end of the play. (I’ve only been watching football for a few years.)
As said earlier, a penalty will be half the distance to the goal. In the NFL at least, defensive pass interference in the end zone places the ball on the 1. I assume in college (I almost never watch college ball) that defensive pass interference in the end zone where the line of scrimmage is on the 15 or closer is half the distance.
Not quite true. Personal fouls are added onto the end of the play. e.g., facemask, late hit on the quarterback, blow to the head, etc.
When does “half the distance” come into effect and when is it the full penalty? I’ve never really known when the rule applies.
It also applies to offensive holding if it occurs past the line of scrimmage. Let’s say it’s 1st & 10 and your guy holds 5 yards downfield. After the 10 yard holding penalty it’ll only be 1st and 15 instead of 1st & 10. The max is 10 yards, and most holding penalties happen on passing plays behind the line of scrimmage so most are a simple 10 yards.
If the ballcarrier earns a first down, is still running, and then a holding happens downfield, the 10 yards are marked off from the spot of the foul and you get 1st & 10, much like a holding penalty on a kick return.
It always applies. Whichever is shorter is what is used. So if you’re on the 22, a 10 yard penalty will get you 10 while a 15 yard penalty will only get you 11, since 22/2 = 11 < 15.
A team can’t score a touchdown by penalty yards. So if the offence is on the 5 yard line and the defensive team takes a penalty that normally carries a 10 yard penalty, it’ll be half the yardage to the goal line. Otherwise, the team on offence would score by a penalty, rather than by putting it across the goal line themselves.
In other words, real men score touchdowns by ramming it down the other guys’ throats, not because of some wussy penalty called by a zebra. 
A team can score a safety (2 points) via penalty: offensive holding* occurring inside the offense’s end zone results in a safety.
*: Probably others types as well, I’m not sure.
Intentional grounding in the end zone is also a safety.
It’s any penalty. Any penalty in the end zone is a safety.