Dice Probability Calculator
Work out the odds of any dice roll. Enter standard dice notation like 2d6+3 or 4d8 and instantly see the chance of hitting a target, the full probability distribution, the average, and the min and max. Perfect for D&D, board games, and any tabletop RPG.
Enter your dice in standard notation (number of dice + d + sides, plus an optional modifier), then choose what you want the odds of. Example: 2d6+3 means roll two six-sided dice and add 3.
* These are the exact mathematical odds for fair, independent dice, computed from every possible combination. Real dice can be very slightly biased, and this tool assumes standard dice with equally likely faces. Results are for learning and game planning — it can't predict any single roll, since each roll is independent of the last.
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What Is a Dice Probability Calculator?
A dice probability calculator works out the exact odds of any dice roll. You type the roll in standard dice notation — like 2d6 (two six-sided dice) or 1d20+5 (one twenty-sided die plus five) — and it instantly tells you the chance of hitting a target number, the average result, the lowest and highest possible totals, and the full probability distribution of every outcome.
It's built for tabletop gamers. Whether you play Dungeons & Dragons, board games, or any RPG, knowing your odds turns guesswork into strategy — should you risk that attack, take the safer option, or push your luck? The math is universal, so it works for any dice and any game, anywhere.
Understanding Dice Notation
Dice notation is the shorthand every RPG uses. It looks like NdS+M:
d = "dice" (just a separator)
S = number of sides on each die
+M = an optional modifier added to the total
Example: 3d6+2 = roll three six-sided dice, add 2
So 1d20 is a single twenty-sided die, 2d6 is two six-sided dice added together, and 4d8−1 is four eight-sided dice with one subtracted. This calculator understands all of it, including a negative modifier.
How to Use This Dice Calculator
- Type your dice in notation, or tap a quick-pick button like 2d6 or 1d20.
- Choose a comparison — at least, exactly, at most, more than, or less than.
- Enter a target number — the result you're hoping to hit or beat.
Click Calculate Odds to see your chance as a percentage, the average roll, and the full distribution chart.
Why 2d6 Isn't the Same as 1d12
Both can give totals from 2 to 12, but the odds are completely different. With 1d12, every number is equally likely — a flat 1-in-12 each. With 2d6, the totals form a bell curve: 7 is the most common result (six ways to make it), while 2 and 12 are rarest (one way each). This is the single most important idea in dice probability — more dice cluster results toward the middle. That's why rolling multiple dice feels more "reliable" than one big die, even at the same range.
Common Dice Odds (Single Die)
| Roll | Chance of Each Number | Average |
|---|---|---|
| 1d4 | 25% | 2.5 |
| 1d6 | 16.67% | 3.5 |
| 1d8 | 12.5% | 4.5 |
| 1d10 | 10% | 5.5 |
| 1d12 | 8.33% | 6.5 |
| 1d20 | 5% | 10.5 |
| 1d100 | 1% | 50.5 |
The 2d6 Distribution Every Gamer Should Know
| Total | Ways to Roll | Chance |
|---|---|---|
| 2 or 12 | 1 | 2.78% |
| 3 or 11 | 2 | 5.56% |
| 4 or 10 | 3 | 8.33% |
| 5 or 9 | 4 | 11.11% |
| 6 or 8 | 5 | 13.89% |
| 7 | 6 | 16.67% |
How Dice Odds Are Calculated
For a single die, each face is equally likely, so the chance of any number is simply 1 divided by the number of sides. For multiple dice, the calculator counts every possible combination and groups them by total. The chance of a given total is the number of combinations that make it, divided by the total number of combinations (which is sidesdice). To get "at least" odds, it adds up the chances of that total and every higher one. This is exact counting, not a simulation, so the numbers are precise.