Two Dice Probability Calculator
Evaluate the probability of rolling specific sums with two fair six-sided dice. Explore exact, at most, or at least probabilities and inspect the full distribution.
Valid sums range from 2 to 12.
Probability: 16.67%
Equivalent odds: 1 in 6.00
| Sum | Combinations | Probability |
|---|---|---|
| 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% |
How to Use This Calculator
- Choose a target sum between 2 and 12.
- Select whether you want P(sum = target), P(sum ≤ target), or P(sum ≥ target).
- Review the calculated probability and the full distribution table.
- Use the results for tabletop games, probability exercises, or statistical demonstrations.
Formula
Total outcomes = 6² = 36
P(sum = k) = combinations achieving k / 36
Combinations follow triangular pattern (1, 2, 3, 4, 5, 6, 5, ... , 1)
Cumulative probabilities are sums of individual probabilities.
Full Description
Rolling two six-sided dice produces sums from 2 to 12 with non-uniform probabilities. This calculator enumerates all outcomes to provide exact probabilities, supporting game odds analysis and probability coursework.
Frequently Asked Questions
Why is 7 the most likely sum?
There are six combinations that produce 7—more than any other sum—making it the modal outcome.
Can I change die sides?
This tool focuses on standard six-sided dice. For other configurations, use the general 6-sided dice probability calculator.
Are dice assumed independent?
Yes. The model assumes fair, independent six-sided dice.
Can probabilities be cumulative?
Select “≤” or “≥” to see cumulative probabilities up to or beyond the target sum.