Dice Probability Calculator
Calculate the probability distribution of dice roll sums for any number of dice and sides.
Probability of rolling 8 or more
41.67%
| Sum | Ways | Probability | Chart |
|---|---|---|---|
| 2 | 1 | 2.78% | |
| 3 | 2 | 5.56% | |
| 4 | 3 | 8.33% | |
| 5 | 4 | 11.11% | |
| 6 | 5 | 13.89% | |
| 7 | 6 | 16.67% | |
| 8 | 5 | 13.89% | |
| 9 | 4 | 11.11% | |
| 10 | 3 | 8.33% | |
| 11 | 2 | 5.56% | |
| 12 | 1 | 2.78% |
See the exact probability of every possible sum when rolling multiple dice, computed with combinatorial math rather than simulation. Set the number of dice, sides per die, and a target sum to see the chance of reaching or beating it.
How to use
- Enter the number of dice and sides per die.
- Enter a target sum to see the probability of rolling that or higher.
- Browse the full distribution table and bar chart below.
Frequently asked questions
- How is this calculated?
- It uses dynamic programming to count the exact number of ways each sum can occur across all dice combinations, then divides by the total number of possible outcomes — no simulation or randomness involved.
- What's the most likely sum for two six-sided dice?
- 7 is the most likely sum for 2d6, since there are 6 ways to make it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total outcomes.
- What does "probability of X or more" mean?
- It's the combined probability of every sum from your target value up to the maximum possible sum, useful for game mechanics like "roll 8+ to succeed".