Dice Roll Calculator
Why 7 Is the Easiest Roll in Craps
Roll two six-sided dice and the sums aren't evenly likely — a total of 7 comes up six times more often than a total of 2 or 12. That's because there's only one way to roll a 2 (1+1), but six different combinations sum to 7. This calculator works out the exact number of ways to reach any target sum, for any number of dice with any number of sides, rather than relying on approximation.
The Method
P = Favorable Outcomes ÷ Total Outcomes
Favorable outcomes are counted by building the full distribution of possible sums across every die, then reading off how many combinations land exactly on, at least, or at most your target.
Two Standard Dice: The Full Distribution
| Sum | Ways to roll it | 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% |
Where This Matters
- Tabletop and casino games — craps, board games, and RPGs all rely on knowing exact dice-sum probabilities to set fair odds and payouts.
- Game design — tuning difficulty by choosing how many dice and what target sums trigger different outcomes.
- Teaching combinatorics — dice sums are a concrete, countable example of how combinations produce non-uniform probability distributions.
- Simulation validation — checking that a dice-rolling script or random number generator matches the true theoretical distribution.
How to Use This Calculator
- Choose Exactly, At Least, or At Most from the dropdown.
- Enter the number of dice being rolled.
- Enter the number of sides per die.
- Enter your target sum.
- Select Calculate to get the exact probability.
Related Calculations
For a single die roll or other equally-likely outcomes, see the Uniform Distribution Calculator. For repeated yes/no trials rather than sums, use the Binomial Distribution Calculator.