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Damage is a number that represents how deadly a threat is. When a creature takes damage, they subtract that amount of damage from their current amount of hit points.
Damage is dealt with attacks and other harmful actions, as well as by a variety of conditions.
Damage rolls
The base damage dealt by a weapon, spell, class action or condition is usually determined by a damage roll. Damage rolls are dice rolls made using the dice specified in the harmful source's description.
Creature add a relevant ability score modifier to the results of their damage rolls, and if they have the relevant proficiency, they also add their proficiency bonus.
Notation
Damage rolls are expressed in the game using both dice notation (xdn, meaning x dice with n sides) and as a damage range ("(x~y)", meaning the roll will result in between x and y damage).
Dice used when making damage rolls is usually any number of dice with a minimum size of d4 and a maximum size of d12.
Damage types
All damage has a damage type, of which there are 13:
A creature's resistances determine what danage types is is immune, resistant or vulnerable towards.
Damage dealt to resistant creatures is halved, whereas damage dealt to vulnerable creatures is doubled.
If a creature is immune to a damage type, they take no damage to it.
If a source of damage mixes different sizes of dice or damage types, they will be listed separately with a plus sign between them.
Sources of damage
A successful attack with a 
Dagger does a base of 1d4
Piercing damage (1~4). This means a single four-sided die 
is rolled to determine the damage, for a total of 1 to 4 piercing damage. Most weapons use a single damage die, but some two-handed weapons use two: a successful attack with a 
Greatsword does 2d6
Slashing damage (2~12), rolling two six-sided dice 
for a total of 2 to 12 slashing damage. Damaging spells typically roll more dice: for example, being caught in a 
will cause 8d6
Fire damage (8~48), though a successful Saving Throw can reduce it to half.
Modifiers
For Weapon attacks, the attacking creature's Ability Score Modifier for Strength or Dexterity is added as a bonus to the total value of the damage roll. For the damage of Spell attacks, no such modifier exists, unless explicitly granted by a magical item, spell, or class feature (such as the Agonising Blast Eldritch Invocation for Warlocks).
The Proficiency Bonus and Advantage mechanics don't apply to Damage Rolls.
Ability Score Modifier
A bonus or penalty may be applied to the result of the roll based on either Strength or Dexterity. For rolls involving multiple dice, such as 2d4, the dice are rolled together, and the modifier is applied to the total result, not to each die.
Whether Strength or Dexterity is used depends on the weapon: usually Strength for melee weapons and Dexterity for ranged weapons. The exceptions to this rule are Finesse weapons, which automatically select Strength or Dexterity, whichever score is higher; and Thrown weapons, which use Strength for both melee and ranged attacks. If a weapon is both Thrown and Finesse, it uses the higher of Strength and Dexterity for both melee and ranged attacks.
Some examples, to make the possible combinations of Finesse and Thrown easier to understand:
- Using a Maul for a melee attack always uses Strength.
- Using a Rapier (Finesse) for a melee attack uses Strength or Dexterity; whichever the attacking creature has a higher score in.
- Shooting a Longbow for a ranged attack always uses Dexterity.
- Throwing a Handaxe (Thrown) for a ranged attack uses Strength.
- Throwing a Dagger (Finesse & Thrown) for a ranged attack uses Strength or Dexterity, whichever is higher.
Whether it's Strength or Dexterity that ends up being used, the following table defines the value of the modifier:
| Ability score | Modifier value | Ability score | Modifier value | |
|---|---|---|---|---|
| 1 | -5 | 16-17 | +3 | |
| 2-3 | -4 | 18-19 | +4 | |
| 4-5 | -3 | 20-21 | +5 | |
| 6-7 | -2 | 22-23 | +6 | |
| 8-9 | -1 | 24-25 | +7 | |
| 10-11 | +0 | 26-27 | +8 | |
| 12-13 | +1 | 28-29 | +9 | |
| 14-15 | +2 | 30 | +10 |
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:
| 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.