Dice Roller
Roll up to ten d4, d6, d8, d10, d12, d20 or d100 dice with a modifier, and see the exact odds of every total — fair rolls from your browser’s secure random generator.
Dice Roller
How to use the dice roller
Pick a die (d4 to d100), set how many to roll with the − and + buttons, and add a modifier if your game uses one — or just
type notation such as 3d8+2 in the notation box. Press Roll, tap the dice or press the space
bar. Six-sided dice show pips; the others show their number on a shape that hints at the real die. The result gives the
total, how it was added up, and the chance of rolling exactly that total or more. Below it, the table lists every possible
total with its exact probability and a bar chart, with your roll highlighted. The last 25 rolls are kept in the history, and
the page address holds your dice and last roll, so Share this result shows a friend the same roll.
Dice notation
Tabletop games write dice as NdS+M: roll N dice with S sides each, add them, then add the modifier M (which can be negative). The same shorthand is used throughout Dungeons & Dragons and most role-playing games.
| Notation | Meaning | Possible totals |
|---|---|---|
d20 | one twenty-sided die | 1 to 20 |
2d6 | two six-sided dice, added | 2 to 12 |
3d8+2 | three eight-sided dice, plus 2 | 5 to 26 |
1d4−1 | one four-sided die, minus 1 | 0 to 3 |
d% or d100 | a percentile roll | 1 to 100 |
How the odds are calculated
Each face of an S-sided die has a 1 in S chance, so N dice have Sⁿ equally likely outcomes. The number of ways to reach each total is counted exactly by convolution: one die makes each value from 1 to S in one way, and every extra die adds the ways for the previous S totals. The counts are kept as exact whole numbers — even 10d100, with 100,000,000,000,000,000,000 outcomes — and divided only at the end:
outcomes = Sⁿ
ways₁(t) = 1 for t = 1 … S
waysₙ(t) = waysₙ₋₁(t − 1) + waysₙ₋₁(t − 2) + … + waysₙ₋₁(t − S)
P(total = t + M) = waysₙ(t) ÷ Sⁿ
average = N × (S + 1) ÷ 2 + M
Each roll itself uses a random whole number from 0 to 4,294,967,295 from crypto.getRandomValues. Six does not
divide 4,294,967,296 evenly (it leaves a remainder of 4), so for a d6 the four highest raw values are redrawn; otherwise
faces 1 to 4 would be very slightly more likely than 5 and 6. The d4 and d8 never need a redraw, because 4 and 8 divide the
range exactly.
Worked example: 2d6+3
You roll 2d6+3 and the dice show 4 and 5: the total is 4 + 5 + 3 = 12. Two six-sided dice have 6 × 6 = 36 outcomes, and a dice sum of 9 can be made in 4 of them (3+6, 4+5, 5+4, 6+3), so the chance of exactly 12 is 4 ÷ 36 = 11.11%, or 1 in 9. A total of 12 or more needs a dice sum of 9, 10, 11 or 12: 4 + 3 + 2 + 1 = 10 ways, so 10 ÷ 36 = 27.78%. The average total is 2 × (6 + 1) ÷ 2 + 3 = 10. These are the numbers the roller shows for this roll.
Why totals bunch up in the middle
One die is flat: every face is equally likely. Two dice make a triangle — 7 can be made six ways but 2 and 12 only one way each — which is why, in board games played with two dice, 6, 7 and 8 come up far more often than 2 or 12. With three or more dice the shape becomes a bell curve: 3d6 gives 10 or 11 with 27 ways each out of 216 (12.5%), but 3 or 18 with a single way each (0.46%). Adding a modifier shifts the whole curve without changing its shape.
Advantage and disadvantage on a d20
In fifth-edition Dungeons & Dragons, advantage means rolling two d20s and using the higher, and disadvantage means using the lower. To hit a target of X or more:
normal: (21 − X) ÷ 20
advantage: 1 − ((X − 1) ÷ 20)²
disadvantage: ((21 − X) ÷ 20)² For a target of 15, a normal roll succeeds 6 ÷ 20 = 30% of the time, advantage 1 − (14 ÷ 20)² = 51%, and disadvantage (6 ÷ 20)² = 9%. To roll with advantage here, choose 2 × d20 and read the higher die. For a simple yes-or-no decision, the coin flip is quicker; to pick between names or options, use spin the wheel, and for any other range of numbers, the random number generator.
Frequently asked questions
How do you read dice notation like 2d6+3?
The number before the “d” is how many dice to roll, the number after it is how many sides each die has, and anything after a + or − is added to or taken from the total. So 2d6+3 means “roll two six-sided dice, add them up, then add 3” — a total from 5 to 15. A missing first number means one die: d20 is the same as 1d20.
What is the most likely total with two dice?
7. Six of the 36 equally likely outcomes add up to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), a chance of 16.67% or 1 in 6. Totals of 2 and 12 each have only one way, 1 in 36 (2.78%).
Is an online dice roller fair?
This one is. Each die uses your browser’s cryptographically secure generator, crypto.getRandomValues, and redraws the rare raw values that would make low faces slightly more likely (modulo bias), so every face has exactly the same chance. The results are not stored or sent anywhere.
What are the odds of rolling a natural 20?
1 in 20 (5%) on a single d20. Rolling two d20s and keeping the higher (advantage) raises it to 1 − (19 ÷ 20)² = 9.75%, and the chance that both dice show 20 is 1 in 400 (0.25%).
How do I roll percentile dice (d100)?
Choose d100 for a number from 1 to 100, each with a 1% chance. Tabletop players often roll percentiles with two ten-sided dice, one for the tens and one for the ones; the d100 here gives the same 1-to-100 range in one roll.