Average dice roll
The average of a fair die sits exactly halfway between its lowest and highest face. For a d20 that is 10.5, and for a d6 it is 3.5.
How to work it out
Add the lowest face to the highest and halve the result. A d8 runs from 1 to 8, so its average is 9 divided by 2, or 4.5. For several dice of the same kind, multiply: three d6 average 10.500000000000002, which is simply 3.5 three times over.
Modifiers move the average by exactly their own value. A 1d8+4 damage roll averages 8.5. Keep and drop rules are the only case where the shortcut fails, because discarding a die pulls the average away from the middle.
Every die
| Die | Range | Average |
|---|---|---|
| D2 | 1 to 2 | 1.5 |
| D3 | 1 to 3 | 2 |
| D4 | 1 to 4 | 2.5 |
| D5 | 1 to 5 | 3 |
| D6 | 1 to 6 | 3.5 |
| D7 | 1 to 7 | 3.9999999999999996 |
| D8 | 1 to 8 | 4.5 |
| D9 | 1 to 9 | 5 |
| D10 | 1 to 10 | 5.500000000000001 |
| D12 | 1 to 12 | 6.5 |
| D14 | 1 to 14 | 7.499999999999999 |
| D16 | 1 to 16 | 8.5 |
| D20 | 1 to 20 | 10.5 |
| D24 | 1 to 24 | 12.5 |
| D30 | 1 to 30 | 15.500000000000002 |
| D50 | 1 to 50 | 25.5 |
| D60 | 1 to 60 | 30.5 |
| D100 | 1 to 100 | 50.5 |
| D120 | 1 to 120 | 60.5 |
Common rolls
- 2d6
- 7
- 3d6
- 10.5
- 4d6 drop lowest
- 12.24
- d20 with advantage
- 13.83
- d20 with disadvantage
- 7.18