Dice Roll Probability Calculator
What is the chance of rolling a particular total with a handful of dice? This calculator builds the exact distribution for any number of fair dice with any number of sides, then reports the probability of hitting your target sum exactly, at least that sum, and at most that sum. It also shows the lowest and highest totals possible.
Dice probability formula
Total outcomes = sides ^ dice
Ways(target) = number of face combinations summing to target
(found by convolving the single-die distribution dice times)
P(total = target) = Ways(target) / total outcomes
P(total ≥ target) = sum of Ways(t) for t ≥ target / total outcomes
P(total ≤ target) = sum of Ways(t) for t ≤ target / total outcomes
The sum of independent uniform dice follows the convolution of their face distributions. The calculator computes the exact count of combinations for each total.
Worked example
Two six-sided dice (36 outcomes) total 7 in six ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1. So P(total = 7) = 6 divided by 36 = 0.1667, about 16.67%. The probability of at least 7 is 21 divided by 36 = 0.5833.
Dice roll probability: frequently asked questions
How is the probability of a dice total found?
Each die is uniform over its faces, and dice are independent, so the distribution of the sum is the convolution of the single-die distributions. The calculator counts the number of face combinations that produce each total and divides by the total number of equally likely outcomes.
Why is 7 the most likely total on two six-sided dice?
There are more face combinations that add to 7 than to any other total: six of them, from 1 and 6 through 6 and 1. With 36 equally likely outcomes, the probability of 7 is 6 divided by 36, about 16.67%, the peak of the triangular distribution.
Does this work for dice with other numbers of sides?
Yes. Set the number of sides to 4, 8, 10, 12, 20, or any value, and the number of dice to any count. The calculator builds the exact distribution for that combination, assuming fair dice.
What totals are possible?
With n dice of s sides, totals range from n, all ones, to n times s, all maximums. Any target outside that range has probability zero, which the calculator reports.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods: Probability distributions.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.