How to use this calculator
Dice totals are not equally likely. There are more ways to make a middle total than an extreme total. This tool builds the full sum distribution by convolution, rather than assuming a uniform sum. Every die has faces numbered 1 through its side count. Dice must be fair, have identical side counts and be independent. Rerolls, dropped dice and bonuses are not included.
The formula
P(sum = t) = number of ordered rolls summing to t / sⁿ
Here p is a probability from 0 to 1, n is a whole number of attempts, C(a,b) counts combinations, and ∏ means multiply all the factors. The input labels define the other symbols.
A worked example
Two fair six-sided dice sum to 7 in 6 of 36 ordered outcomes: 16.67%.
Does this predict what I will get?
No. It describes a probability under the rules you enter. A single run can differ from the average. A displayed rounded 100% may still be slightly below certainty unless the model includes a guarantee.
Where do the rates come from?
You enter them. Check the rules and rate disclosure for your exact outcome. We do not supply odds for real products, collect account details or fetch rates from a game or seller.