Dice Roller
A dice roller for up to 20 dice from d4 to d100, with a modifier or notation like 2d6+3: every die, the total, and the exact chance of rolling that total or higher.
Total (2d6)
- Each die (2d6)
- 4, 5
- Total
- 9
- Possible totals All ones to all 6s. There are 36 equally likely ways for 2 dice to land.
- 2 to 12
- Average total Each d6 averages (6 + 1) / 2 = 3.5, so 2 of them average 7. Standard deviation 2.42.
- 7
- Chance of exactly 9 The number of ways 2 dice can sum to 9, over all 36 outcomes.
- 4 in 36 (11.11%)
- Chance of 9 or higher What a check against a target of 9 would succeed on with 2d6.
- 10 in 36 (27.78%)
- Chance of 9 or lower
- 30 in 36 (83.33%)
| Total | Ways | Chance | This or higher |
|---|---|---|---|
| 2 | 1 | 2.78% | 100% |
| 3 | 2 | 5.56% | 97.22% |
| 4 | 3 | 8.33% | 91.67% |
| 5 | 4 | 11.11% | 83.33% |
| 6 | 5 | 13.89% | 72.22% |
| 7 | 6 | 16.67% | 58.33% |
| 8 | 5 | 13.89% | 41.67% |
| 9 | 4 | 11.11% | 27.78% |
| 10 | 3 | 8.33% | 16.67% |
| 11 | 2 | 5.56% | 8.33% |
| 12 | 1 | 2.78% | 2.78% |
How the Dice Roller works
This dice roller rolls up to 20 dice of 4, 6, 8, 10, 12, 20 or 100 sides, adds a modifier, and shows each die, the total, and the exact chance of that total. Typed notation such as 2d6+3 (two six-sided dice plus 3) or d20-1 works too, with any number of sides from 2 to 1,000.
The odds come from counting. Two six-sided dice can land 36 ways, and a total of 7 or higher comes from 21 of them, which is 58.33%. For more dice the counting is done by convolution: the number of ways to make each total on three dice is built from the counts for two dice, one die at a time, which is exact for any pool up to 20d100 and its 10^40 outcomes.
Adding dice changes the shape. One d20 gives every face 5%. Three d6 average 10.5, the same as a d20, but they pile up in the middle: 10 and 11 each come up 27 times in 216, or 12.5%, and an 18 needs all three sixes, 1 time in 216. The average of n dice with s sides is n(s + 1)/2, so 3d6 is 3 x 3.5 = 10.5 and 2d6+3 is 10.
The d20 check is the core of fifth-edition Dungeons & Dragons, and the main job of a DnD dice roller. Roll a d20, add your modifier, and compare the total with the target number (the DC, or the armor class for an attack). Meeting or beating it succeeds. With a +5 against DC 15 you need 10 or more on the die, which is 11 faces of 20, or 55%. Each point of modifier is worth exactly 5 percentage points, as long as the face you need stays between 2 and 20.
Advantage means rolling two d20 and keeping the higher; disadvantage means keeping the lower. If you need k or more on the die, one die succeeds with probability (21 - k) / 20. Advantage fails only when both dice fail, so it succeeds with probability 1 - ((k - 1) / 20)^2. Disadvantage needs both dice to succeed, so its probability is ((21 - k) / 20)^2. Advantage helps most in the middle and much less at the ends. Over many rolls, advantage averages 13.825 on the die and disadvantage 7.175. In the fifth-edition rules, advantage and disadvantage cancel when you have both, and two sources of advantage still roll only two dice.
What this online dice roller does not do: exploding dice, rerolling ones, or keeping the highest few of a pool. A physical d10 is usually numbered 0 to 9, with the 0 read as 10; here a d10 shows 1 to 10 and a d100 shows 1 to 100.
Dice Roller FAQ
How much does advantage help on a d20?
Up to 25 percentage points, when you need an 11: one die succeeds 50% of the time and the higher of two succeeds 75%. That is the same as a +5 bonus. The formula is 1 - ((k - 1) / 20)^2 for needing k or more. Needing a 20, advantage only lifts the chance from 5% to 9.75%.
What are the odds of rolling a natural 20?
5% on one d20, or 1 in 20. With advantage it is 1 - 0.95^2 = 9.75%, and with disadvantage 0.05^2 = 0.25%, or 1 in 400.
What is the most likely total on two dice?
7. Six of the 36 ways two six-sided dice can land add up to 7, so it comes up 16.67% of the time, or 1 in 6. 2 and 12 are the least likely, one way each.
What does 2d6+3 mean?
Roll two six-sided dice, add them, and add 3. The total runs from 5 to 15 and averages 10.
How do I roll 4d6 and drop the lowest?
Roll four six-sided dice and add the three highest. This dice roller totals all four, so take the lowest die off yourself.
Is a virtual dice roller fair?
This one gives every face exactly the same chance. Each die comes from your browser's cryptographically secure random generator. A physical die is only as fair as it is evenly made and thrown.