Dice Probability Calculator
Enter how many dice you roll and how many sides they have. Choose a target sum or a range to see the exact chance of landing on that total.
Supports up to 10 fair dice without approximation.
Valid totals range from 2 to 12.
P(total = 7)
16.67%
Exact sum probability
P(2 ≤ total ≤ 12)
100.00%
Inclusive cumulative likelihood
Possible Totals
2 – 12
Range of outcomes
| Total | Probability |
|---|---|
| 2 | 2.78% |
| 3 | 5.56% |
| 4 | 8.33% |
| 5 | 11.11% |
| 6 | 13.89% |
| 7 | 16.67% |
| 8 | 13.89% |
| 9 | 11.11% |
| 10 | 8.33% |
| 11 | 5.56% |
| 12 | 2.78% |
How to Use This Calculator
- Enter the number of identical fair dice and the number of sides on each die.
- Specify a target sum to view the exact probability of rolling that value.
- Optionally set a start and end value to compute the chance of landing inside a range.
- Review the distribution table to understand how probabilities change across totals.
Formula
The calculator enumerates every outcome via dynamic programming. The count of ways to reach a sum t with n dice equals the sum of ways to reach t − face with n − 1 dice across all faces.
waysn(t) = ∑face=1s waysn−1(t − face)
P(total = t) = waysn(t) / sⁿ
This exact approach avoids normal approximations and is precise for up to 10 dice with up to 20 sides each.
Full Description
Probability distributions for dice underpin countless strategy games and probability puzzles. While the average of multiple dice trends toward the center, the exact shape of the distribution depends on how many dice you roll and how many faces each has. This tool provides exact results without requiring manual convolution or spreadsheets.
Use the calculator to evaluate the odds of critical hits in tabletop RPGs, to analyze board game mechanics, or to explore combinatorics examples in statistics classes. Because results are calculated exactly, you can trust them for precise probability comparisons.
Frequently Asked Questions
Can I use different dice types together?
The current version assumes all dice are identical. For mixed dice, convolve each die type separately or run multiple calculations and combine them manually.
Why is there a limit of 10 dice?
Enumerating outcomes grows exponentially. Limiting the inputs keeps the calculation fast and responsive in the browser while remaining exact.
Do biased dice work?
This tool assumes fair dice with equal probability for each face. Biased dice require weighted distributions, which are not currently supported.
How accurate is the range probability?
Range probabilities sum the exact probabilities for each total inside the range. The result is an exact cumulative probability for the specified bounds.