Average of one die, then scale it up
A fair die is symmetric, so its average is just the midpoint of its faces: (sides + 1) ÷ 2. A d6 averages (6 + 1) ÷ 2 = 3.5. Rolling several dice, the averages simply add, so N dice with S sides average N times the single-die value. Any flat modifier gets added at the end.
Average by die type
| Die | Range | Average | Std. deviation |
|---|---|---|---|
| d4 | 1–4 | 2.5 | 1.12 |
| d6 | 1–6 | 3.5 | 1.71 |
| d8 | 1–8 | 4.5 | 2.29 |
| d10 | 1–10 | 5.5 | 2.87 |
| d12 | 1–12 | 6.5 | 3.45 |
| d20 | 1–20 | 10.5 | 5.77 |
For mixed pools, add the die averages: d6 + d8 averages 3.5 + 4.5 = 8. The 3d6 total averages 3 × 3.5 = 10.5, with a range of 3 to 18.
Average is not the most likely single roll
- One die is flat. Every face of a single d20 is equally likely, so 10.5 is the average but no value is favored.
- Many dice bunch up. Roll several and the totals cluster near the average in a bell shape. On 2d6 a seven comes up six times as often as a two.
- Modifiers move, not spread. A +5 lifts the average, min and max by five, but the variability is unchanged.
Common questions
What is the average roll of a six-sided die?
It is 3.5, from (1 + 6) divided by 2. No single roll ever lands on 3.5, but over many rolls the results average out to it.
What is the average of 3d6?
Ten and a half. Each d6 averages 3.5, so three of them average 3 times 3.5, which is 10.5. Add any modifier straight on top: 3d6 + 2 averages 12.5.
Does a plus or minus modifier change the spread?
No. A modifier shifts the average, the minimum and the maximum all by the same amount, but the standard deviation, how spread out the results are, stays exactly the same.
