How Dice Probability Is Calculated
When you roll multiple dice, the sums are not equally likely — a sum near the middle of the possible range has many more ways to occur than a sum at the extremes. This calculator counts, exactly, every possible combination of rolls that produces each sum.
The Method
The tool builds the full probability distribution of the sum using combinatorics (a technique called convolution): starting from one die’s distribution, it repeatedly combines it with another die to build up the distribution for all the dice together. It then divides the number of favorable combinations by the total number of possible rolls (sides^number of dice) to get an exact probability.
- Works for standard 6-sided dice or any custom number of sides.
- “At least” and “at most” add up probabilities across a range of sums.
Provided for general educational and recreational use, such as tabletop games and probability practice.