A dice average calculator saves you doing XdY+Z sums in your head mid-session. 2d6+3 averages 10. 8d6, the classic fireball, averages 28. 4d6 drop the lowest, the most popular way to roll ability scores, averages 12.24, nearly two points better than a straight 3d6. And advantage on a d20 lifts the average from 10.5 to 13.83. Type in your dice, pick how they’re counted, and the free calculator above gives the average, the range and the spread.
How the dice average calculator works
One die with Y sides averages (Y + 1) ÷ 2: 3.5 for a d6, 10.5 for a d20. Add X of them and the average is X times that, plus any modifier. The spread grows more slowly than the total, which is why 3d6 clusters around 10 and 11 while 1d20 is flat.
Average of XdY + Z = X × (Y + 1) ÷ 2 + Z Standard deviation = √(X × (Y² − 1) ÷ 12)
Dropping or keeping dice changes things. The average of the highest of X dice is Σ (1 − ((k − 1) ÷ Y)^X) over every face k, and the lowest is the mirror image. Drop the lowest is simply all the dice minus the lowest one.
Handy averages
| Roll | Average |
|---|---|
| 1d4 / 1d6 / 1d8 | 2.5 / 3.5 / 4.5 |
| 1d10 / 1d12 / 1d20 | 5.5 / 6.5 / 10.5 |
| 2d6 | 7 |
| 3d6 | 10.5 |
| 4d6 drop lowest | 12.24 |
| d20 with advantage | 13.83 |
| d20 with disadvantage | 7.18 |
| 8d6 | 28 |
The average is only half the story for a d20 check, because what matters is whether you beat a target. For chances of hitting a specific total, the dice probability calculator gives the full distribution. Need to actually roll? The dice roller does any combination.
Rather roll them than average them? The DnD stat roller rolls 4d6 drop lowest six times and shows the point-buy value, and the DnD dice roller handles any other roll.