Dice Roll Probability Calculator
Dice Roll Probability Calculator
Enter how many dice you're rolling, how many sides each die has, and the sum total you want the probability for. This calculates the exact number of ways to reach that sum, the total number of possible outcomes, and the resulting probability.
This is a probability calculator, not a dice roller: instead of simulating one random roll, it counts every possible combination of die faces across all your dice to work out exactly how likely a given sum is — the same math behind why 7 is the most common result rolling two standard six-sided dice, and why board games and tabletop RPGs weight certain totals more heavily than others. Because it uses exact combinatorial counting rather than simulation, the result is precise even for sums that are individually rare.
- Different from a Dice Roller: a dice roller simulates an actual random roll, while this calculator computes the underlying probability math — how likely a given sum is across all possible rolls.
- Uses exact combinatorial counting: rather than estimating through simulation, this counts every possible combination of die faces that produces the target sum.
- Common use case: board game and tabletop RPG strategy (knowing your odds before committing to a dice-dependent action), as well as understanding classic probability puzzles like the 2d6 bell curve.
Why is a sum of 7 the most likely outcome with two six-sided dice?
Because more combinations of two dice add up to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1 — six ways) than any other sum, while extreme sums like 2 or 12 have only one possible combination each.
What happens if I enter a target sum that's impossible for the given dice?
If the target sum is below the minimum possible (number of dice) or above the maximum possible (dice × sides), the number of ways to reach it is 0, giving a 0% probability.
Dice Roll Probability Calculator
Enter how many dice you're rolling, how many sides each die has, and the sum total you want the probability for. This calculates the exact number of ways to reach that sum, the total number of possible outcomes, and the resulting probability.
This is a probability calculator, not a dice roller: instead of simulating one random roll, it counts every possible combination of die faces across all your dice to work out exactly how likely a given sum is — the same math behind why 7 is the most common result rolling two standard six-sided dice, and why board games and tabletop RPGs weight certain totals more heavily than others. Because it uses exact combinatorial counting rather than simulation, the result is precise even for sums that are individually rare.
- Different from a Dice Roller: a dice roller simulates an actual random roll, while this calculator computes the underlying probability math — how likely a given sum is across all possible rolls.
- Uses exact combinatorial counting: rather than estimating through simulation, this counts every possible combination of die faces that produces the target sum.
- Common use case: board game and tabletop RPG strategy (knowing your odds before committing to a dice-dependent action), as well as understanding classic probability puzzles like the 2d6 bell curve.
Why is a sum of 7 the most likely outcome with two six-sided dice?
Because more combinations of two dice add up to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1 — six ways) than any other sum, while extreme sums like 2 or 12 have only one possible combination each.
What happens if I enter a target sum that's impossible for the given dice?
If the target sum is below the minimum possible (number of dice) or above the maximum possible (dice × sides), the number of ways to reach it is 0, giving a 0% probability.