Calculate the probability of rolling a specific sum with one or more dice of any polyhedral type.
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Probability
Rolling 2d6, the probability of getting a sum of 7 is 16.67%.
How dice probability works
Each die has an equal chance of landing on any face. When rolling multiple dice, the total number of outcomes grows exponentially while only some combinations produce the target sum. Sums near the middle of the range are more likely because more combinations add up to them, while extreme values (all ones or all sixes) have only one way to occur.
Also in Probability
Probability
A dice probability calculator determines the likelihood of rolling a specific total when throwing one or more dice. It counts the number of favorable outcomes using dynamic programming and divides by the total number of possible outcomes to give an exact probability.
A single fair die with S sides gives each face an equal probability of 1/S. Rolling a 4 on a standard six-sided die has probability 1/6 ≈ 16.67%. Every outcome from 1 to S is equally likely.
For non-standard dice (d4, d8, d10, d12, d20), the same logic applies: each face has probability 1/S, and the possible sums range from 1 to S.
P(target) = 1 / S
Probability of rolling a specific value on a single die with S sides.
With multiple dice, the total outcomes grow exponentially (S^N for N dice with S sides), but favorable outcomes for each sum vary. Sums near the middle of the range are more probable because more combinations produce them. For 2d6, the sum of 7 has 6 favorable outcomes out of 36 total (16.67%), while 2 and 12 each have only 1 (2.78%).
The calculator uses dynamic programming to count exactly how many ways N dice can produce each sum, avoiding the need to enumerate all outcomes individually.
Total outcomes = S^N
The total number of possible outcomes when rolling N dice with S sides each.
P(sum) = favorable outcomes / total outcomes
The probability of rolling a specific sum.
Frequently asked questions
The most likely sum is 7, with 6 out of 36 possible outcomes (16.67%). The six combinations are: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
Yes. Enter any number of sides (4, 8, 10, 12, 20, or any other value) and the calculator computes exact probabilities for that die type.
Extreme sums like all-ones or all-sixes require every die to land on the same face, giving only one way to achieve them. Middle sums can be reached through many different combinations of die faces, making them far more probable.
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