Dice Probability Calculator
The dice probability calculator computes the probability of rolling a target sum using N dice each with S sides. Enter the number of dice, sides per die, and optionally a target sum. The calculator displays the probability distribution for all possible sums. For example, rolling two 6-sided dice (2d6) can produce sums from 2 to 12. The sum of 7 has the highest probability (6/36 ≈ 16.67%) because it can be rolled six ways.
Probability distribution
Dice probability calculator: frequently asked questions
What is the probability of rolling a specific sum?
The probability depends on the number of dice and sides per die. For example, rolling two 6-sided dice: there are 36 possible outcomes, and only 1 way to get a sum of 2 (1+1), so P(sum=2) = 1/36 ≈ 2.78%.
Why are some sums more likely than others?
Sums in the middle have more ways to be rolled. For two 6-sided dice, a sum of 7 can be rolled 6 ways: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). A sum of 2 can only be rolled 1 way: (1,1).
How many possible outcomes are there?
With N dice each having S sides, there are S^N total possible outcomes. For example, 2 six-sided dice have 6^2 = 36 outcomes.
What is a 20-sided die?
A d20 (20-sided die) is used in role-playing games. It has sides numbered 1-20. Each outcome has equal probability (1/20 = 5%).
Can this calculator handle more than 5 dice?
Yes, but the number of outcomes grows exponentially. Five 6-sided dice have 6^5 = 7,776 outcomes. More dice make probabilities small and calculations slower.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.