Average Dice Rolls: d4 to d100 Cheat Sheet
The average roll of any die is (sides + 1) / 2: a d4 averages 2.5, d6 3.5, d8 4.5, d10 5.5, d12 6.5, d20 10.5 and d100 50.5. For several dice, multiply by the number of dice and add any modifier, so 2d6+3 averages 10 and 8d6 averages 28.
What is the average roll of each die?
Every standard die has faces numbered from 1 up to its size, each equally likely. The average is the midpoint of the lowest and highest face. This is the quick reference, and you can roll any of these in the dice calculator.
| Die | Range | Average | Common uses in 5e |
|---|---|---|---|
| d4 | 1–4 | 2.5 | Dagger, Magic Missile darts, Bless |
| d6 | 1–6 | 3.5 | Shortsword, Sneak Attack, Fireball |
| d8 | 1–8 | 4.5 | Longsword, rapier, Cure Wounds |
| d10 | 1–10 | 5.5 | Heavy crossbow, Eldritch Blast, Fire Bolt |
| d12 | 1–12 | 6.5 | Greataxe, Barbarian hit die |
| d20 | 1–20 | 10.5 | Attack rolls, checks, saves |
| d100 | 1–100 | 50.5 | Random tables, Wild Magic |
What is the formula for the average dice roll?
For one die with X sides, the average is (X + 1) / 2. A d8 has faces 1 to 8, so its average is (8 + 1) / 2 = 4.5. Notice the result is never a whole number for the standard dice, because each has an even number of faces.
For a full expression written as NdX+M, the average is:
Average = N × (X + 1) / 2 + M
- Find the average of one die.
- Multiply by the number of dice.
- Add the flat modifier once (not once per die).
So 2d8+3 is 2 × 4.5 + 3 = 12. If an expression mixes dice, average each part and add them: 1d6+1d4 is 3.5 + 2.5 = 6. If you are unsure how to read an expression, the dice notation guide breaks it down.
Why is the average not a number you can roll?
An average of 3.5 on a d6 doesn't mean you ever roll 3.5. It means that over many rolls, the results balance out to 3.5 per die. Half of all d6 rolls are 1, 2 or 3 and half are 4, 5 or 6, so the midpoint sits between 3 and 4. Once you add several dice together, the average often becomes a whole number again, as with 2d6 (7) or 8d6 (28), and it is usually among the most likely totals.
What are the averages of common 5e damage rolls?
Every value below was calculated exactly from all possible outcomes.
| Roll | Example | Range | Average |
|---|---|---|---|
| 1d4+1 | One Magic Missile dart | 2–5 | 3.5 |
| 3d4+3 | Magic Missile, all three darts | 6–15 | 10.5 |
| 1d6+2 | Scimitar or shortsword, +2 modifier | 3–8 | 5.5 |
| 1d8+3 | Longsword or rapier, +3 modifier | 4–11 | 7.5 |
| 1d10+4 | Heavy crossbow or glaive, +4 modifier | 5–14 | 9.5 |
| 1d12+3 | Greataxe, +3 modifier | 4–15 | 9.5 |
| 2d6 | Greatsword or maul, no modifier | 2–12 | 7 |
| 2d6+3 | Greatsword, +3 modifier | 5–15 | 10 |
| 2d8+3 | Longsword critical hit, +3 modifier | 5–19 | 12 |
| 3d6 | Sneak Attack at 5th level | 3–18 | 10.5 |
| 3d8 | Shatter at 2nd level | 3–24 | 13.5 |
| 8d6 | Fireball or Lightning Bolt at 3rd level | 8–48 | 28 |
| 10d6 | Fireball cast with a 5th-level slot | 10–60 | 35 |
| 4d6 drop lowest | Rolling one ability score | 3–18 | 12.24 |
| 2d20 keep highest | A d20 with advantage | 1–20 | 13.83 |
| 2d20 keep lowest | A d20 with disadvantage | 1–20 | 7.18 |
The keep and drop rows can't use the simple formula, because discarding a die changes which results are possible. Their averages come from counting every combination. Spell damage figures are for the base spell; see Fireball and Magic Missile for scaling.
Why do monster stat blocks list average HP and damage?
Monster stat blocks give each hit point total and attack damage as a fixed number followed by the dice in parentheses, such as "7 (2d6)". The fixed number is the average of the dice, rounded down. It exists so the DM can skip rolling.
- Speed: running a fight with eight goblins goes faster when every attack simply deals its listed damage.
- Predictability: fixed damage makes it easier to judge how dangerous an encounter is. The encounter calculator works the same way, from fixed numbers.
- Choice: the dice are still printed, so a DM who wants swingier fights or a tougher boss can roll instead.
Examples of the rounding
In the 2014 Monster Manual, a goblin has 7 (2d6) hit points, and its scimitar deals 5 (1d6+2). The true average of 1d6+2 is 5.5, which rounds down to 5. An ogre has 59 (7d10+21) hit points; the exact average is 59.5.
How do you work out average damage per attack?
The damage average assumes you hit. To compare weapons or builds fairly, multiply by your chance to hit, then add the extra from critical hits.
Suppose you need an 8 to hit with a 1d8+3 longsword. You hit on 8 through 19 (60%) for an average of 7.5, and crit on a natural 20 (5%) for 2d8+3, which averages 12. Expected damage per swing is 0.60 × 7.5 + 0.05 × 12 = 5.1. On a critical hit only the dice are doubled; the modifier is added once. More on that in critical hits in 5e.
Is 2d6 better than 1d12?
For damage, slightly. 2d6 averages 7 and 1d12 averages 6.5. 2d6 also clusters around its average, while 1d12 is just as likely to roll a 1 as a 12. The full breakdown is in 2d6 and 3d6 probability tables.
What is the average healing from common spells and potions?
Healing uses the same formula. Here the editions differ, so check which rules your table uses.
- Potion of Healing: 2d4+2, average 7.
- Cure Wounds, 2014 rules: 1d8 plus your spellcasting modifier. With a +3 modifier that averages 7.5.
- Cure Wounds, 2024 rules: 2d8 plus your spellcasting modifier. With a +3 modifier that averages 12.
Each higher spell slot adds more dice, and every extra d8 adds 4.5 to the average. See Cure Wounds for the full scaling.
When should you use the average instead of rolling?
- Monster HP and damage: most DMs use the listed averages for regular enemies.
- Leveling up: the rules let you take a fixed hit point increase instead of rolling your hit die. That fixed value is the die's average rounded up (for example 5 for a d8, 7 for a d12), slightly better than the true average.
- Comparing options: averages are the fastest way to see which spell or weapon deals more damage over time.
Averages tell you what happens over many rolls. In a single roll, anything in the range can happen, which is why the dice are still fun to roll.
FAQ
What is the average roll of a d20?
10.5. A d20 has faces 1 to 20, and (20 + 1) / 2 = 10.5. With advantage the average rises to about 13.83, and with disadvantage it drops to about 7.18.
What is the average of 2d6?
7. Each d6 averages 3.5, and two of them average 7. It is also the most common 2d6 total.
How do you calculate average damage in 5e?
Add (sides + 1) / 2 for every damage die, then add the flat modifier once. A longsword with +3 Strength, 1d8+3, averages 4.5 + 3 = 7.5.
Why do monster stat blocks show a number before the dice?
The number is the average of the dice expression, rounded down. A DM can use it instead of rolling, for example a goblin's 2d6 hit points are listed as 7.
Is 2d6 better than 1d12?
On average, slightly. 2d6 averages 7 while 1d12 averages 6.5, and 2d6 is more consistent because its results cluster around 7.
Related
- Dice Calculator
- Dice Notation Guide: What 2d6+3 Means and How to Read Any Roll
- 2d6 and 3d6 Probability Tables
- Critical Hits in 5e: How Crit Damage Works
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