6-Sided Dice Probability Calculator
Select the number of six-sided dice, choose a target sum, and evaluate exact probabilities for less than, equal to, or greater than conditions.
Probability: 16.6667%
Equivalent odds: 1 in 6.00
| Total | Combinations | Probability |
|---|---|---|
| 2 | 1 | 2.7778% |
| 3 | 2 | 5.5556% |
| 4 | 3 | 8.3333% |
| 5 | 4 | 11.1111% |
| 6 | 5 | 13.8889% |
| 7 | 6 | 16.6667% |
| 8 | 5 | 13.8889% |
| 9 | 4 | 11.1111% |
| 10 | 3 | 8.3333% |
| 11 | 2 | 5.5556% |
| 12 | 1 | 2.7778% |
How to Use This Calculator
- Specify how many six-sided dice you plan to roll.
- Set the target sum to evaluate.
- Choose whether to compute P(sum ≤ target), P(sum = target), or P(sum ≥ target).
- Review the report and explore the full distribution table for additional context.
Formula
P(sum = k) = number of solutions to x₁ + ... + xn = k with 1 ≤ xᵢ ≤ 6, divided by 6ⁿ
Probability types use cumulative sums of the distribution as needed.
Combinatorial counts computed via recursive inclusion.
Full Description
The sum of multiple d6 rolls follows a discrete distribution whose shape approaches normality as more dice are added. This calculator enumerates all combinations to deliver exact probabilities, useful for tabletop games or probability lessons.
Frequently Asked Questions
How large can the dice count be?
The recursive enumeration works best for small to moderate dice counts (e.g., up to ~6–8). Larger counts may become slow.
Are dice assumed fair?
Yes. Each face from 1 to 6 is equally likely.
Can this handle modifier terms?
Not currently. Add modifiers manually after obtaining probabilities for the raw sum.
Does it support "at least" probabilities?
Yes. Select “Sum ≥ target” for the probability of rolling at least the specified total.