What the calculator shows
This DnD dice calculator takes any roll in dice notation and draws the chance of every total, the same picture as on our spell and monster pages. Under it:
- Average: what the roll comes to over many throws.
- Range: the lowest and highest totals it can make.
- Most likely: the single total that comes up most.
- Typical swing: how far from the average a roll usually lands (the standard deviation).
- Chance of at least: set a target, like an Armor Class or a save DC, and see how often you reach it. Bars below the target are dimmed.
Press Roll it and the total lights up on the chart, so you can see whether it was a lucky roll or an ordinary one.
Averages without a calculator
One die averages half of one more than its sides: a d6 is 3.5, a d8 is 4.5, a d20 is 10.5. Add the averages of every die, then the modifier. 2d6+3 is 3.5 + 3.5 + 3 = 10. 8d6, a Fireball, is 28.
Keeping or dropping dice breaks that shortcut, which is what the calculator is for. 4d6 drop the lowest averages 12.24, not 14, and advantage averages 13.82.
Why more dice make a bell curve
A single d20 is flat: every number from 1 to 20 is 5%. Add dice together and the middle totals pile up, because there are more ways to make them. A 7 on 2d6 can be 1+6, 2+5, 3+4 and the reverse, six ways out of 36. A 2 has only one way. The more dice you add, the taller and narrower the bell.
That is why 3d6 rolls a 9 to 12 almost half the time (48.1%), while a d20's results are spread evenly from 1 to 20.
Greatsword or greataxe?
The old argument: 2d6 (greatsword) or 1d12 (greataxe)? Compare them above. 2d6 averages 7 to the greataxe's 6.5, and rolls higher 50% of the time, ties 8.3%, and loses 41.7%. The greataxe swings wider: its typical swing is ±3.5 against ±2.4, so it hits 12 more often (8.3% against 2.8%). The greatsword is steadier.
Advantage, in numbers
| Roll | Average | 11 or more | 15 or more |
|---|---|---|---|
| d20 | 10.5 | 50% | 30% |
| Advantage (2d20kh1) | 13.82 | 75% | 51% |
| Disadvantage (2d20kl1) | 7.18 | 25% | 9% |
Against a DC of 15, advantage turns a 30% chance into 51%. It has its own roller.
Rolling stats: 3d6 or 4d6 drop lowest
| Method | Average | 15 or more | 8 or less |
|---|---|---|---|
| 3d6 | 10.5 | 9.3% | 25.9% |
| 4d6 drop lowest | 12.24 | 23.1% | 10.5% |
Dropping the lowest die gives a score of 15 or more two and a half times as often. The stat roller rolls all six at once.
Writing a roll
The calculator reads the same notation as the dice generator: 2d6+3, 4d6kh3 (keep the highest three), 2d20kl1 (keep the lowest one), 1d8+1d6+2, and d100 or d%. The Dice Notation Guide explains every part.