Damage

For a comprehensive summary of the mechanics behind all rolls and modifiers, see: Die Rolls

A Damage Roll happens when the game wants to determine the damage done by a successful attack, area of effect spell, trap, and so on. It can involve one or many dice of any type. This is not to be confused with the Attack Roll, which is a D20 roll deciding whether the attack hits at all.

For example, a successful hit with a Dagger will lead to a d4 being rolled to determine the damage (referred to as 1d4 damage), whereas a successful attack with a Greatsword will lead to two d6 being rolled (referred to as 2d6) for a total damage of 2 to 12. Being caught in a Fireball will cause 8d6 points of damage, though a successful Saving Throw can reduce it to half.

For attacks made with Weapons, various Modifiers can affect the total value of the roll, such as the attacking creature's Ability Score Modifier, Proficiency Bonus, or Advantage / Disadvantage. For the damage of spell attacks, no such modifiers apply.

The Ability Score used for the Modifier of a weapon attack is either Strength or Dexterity, depending on the weapon. Melee weapons use the Strength Modifier, unless they have the Finesse property (such as Dagger or Rapier), in which case Dexterity can be used instead. The same rules apply to melee weapons with the Thrown property (such as Dagger or Handaxe) when they're thrown for a ranged attack: they use the Strength modifier, unless they have both Thrown and Finesse (such as Dagger), in which case Dexterity can be chosen again. Regular ranged weapons (such as Bows and Crossbows) always use Dexterity.

For rolls involving multiple dice, such as 2d4, the multiple dice are rolled together, and this is considered a single roll insofar Modifiers are concerned. For example, the Proficiency Bonus will be applied to the total result of the 2d4 roll, not to each d4 roll. Similarly, when Advantage applies, the entire 2d4 roll is done twice, and the higher of the two totals is taken.

A bit of Mathematics

Note that due to the mathematics of dice rolls, the difference between, say, 1d8 and 2d4 is more than just the higher minimum value of 2 on the 2d4 roll. With the d8, you have an equal chance of getting, say, a 5 and an 8. On the other hand, the 2d4 roll is statistically more likely to lead to a total value of 5, than a total value of 8. This is most easily explained with a table of all possible outcomes:

Possible results of a 2d4 roll, highlighting the number of possibilities resulting in a total value of 5

First roll	Second roll	Total value
1	1	2
1	2	3
1	3	4
1	4	5
2	1	3
2	2	4
2	3	5
2	4	6
3	1	4
3	2	5
3	3	6
3	4	7
4	1	5
4	2	6
4	3	7
4	4	8

Notice how often the 5 appears in the possibilities for the total value (4 out of 16 possibilities) vs. how often the 8 appears (1 out of 16). This means a 2d4 roll has a 25% chance of resulting in 5 points of damage, but only a 6.125% chance of resulting in 8 points of damage. Meanwhile, the 1d8 roll actually has a higher chance of resulting in the maximum damage value of 8, since 1 out of 8 possibilities (12.5%) result in an 8.