Dice Probability Calculator
Calculate the probability of rolling a specific sum with any number of dice. Whether you play board games, tabletop RPGs, or study probability, this calculator gives you exact probabilities for any combination of standard polyhedral dice.
Dice probability is a fundamental concept in combinatorics and probability theory. When rolling multiple dice, the number of ways to achieve a particular sum follows a discrete probability distribution.
How it works: For n dice with s sides each, the total number of possible outcomes is s^n. The calculator uses dynamic programming to count exactly how many of those outcomes produce each possible sum, from n (all ones) to n x s (all maximum). This gives exact probabilities, not approximations.
Applications: Dice probabilities are essential in game design and balance, tabletop RPGs like Dungeons & Dragons, gambling analysis, and teaching introductory probability. For example, with 2d6, the most likely sum is 7 (probability 1/6), while 2 and 12 each have probability 1/36.