Dice Probability Calculator
Calculate the probability of rolling a specific total with any number of dice.
Calculate the probability of rolling a specific total with any number of dice.
How Dice Probability Calculator Works
Every possible combination of individual die results is counted, and the ones that add up to your target sum are identified — dividing that count by the total number of possible outcomes (the number of sides raised to the number of dice) gives the probability.
See It In Action
Who Uses Dice Probability Calculator and Why
- Calculating the odds of rolling a specific total when designing or playing a tabletop or board game.
- Verifying a probability assumption used in a game design exercise involving multiple dice.
- Teaching or reviewing how combinatorics applies to summing multiple independent dice rolls.
Mistakes to Avoid
- Assuming every possible sum is equally likely — sums in the middle of the possible range (like 7 with two six-sided dice) have far more ways to occur than sums at the extremes (like 2 or 12), which each have only one combination.
- Forgetting that adding more dice or changing the number of sides per die changes both the range of possible sums and how the probabilities are distributed across that range.
- Miscounting the total number of possible outcomes — it's the number of sides raised to the power of the number of dice (not multiplied), which is easy to get wrong for larger dice counts.
Tips for Best Results
- With two standard six-sided dice, 7 is the most probable single sum, since six different combinations (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) produce it out of 36 total possible combinations.
- As you add more dice, the distribution of possible sums becomes increasingly bell-shaped, with sums near the middle of the range becoming disproportionately more likely than the extremes.
Fixing Common Problems
I expected all sums to have roughly equal probability but they don't. — This is expected behavior, not an error — middle-range sums have many more ways to be formed from the individual dice than extreme sums (the minimum and maximum possible totals each have only one combination), so they're always more probable.
Terms Explained
Sample space: The complete set of every possible outcome for a given roll of one or more dice.
Standard die: A die with faces numbered 1 through its number of sides, each equally likely on a fair roll — the default assumption for this calculator.