How to use it
- Set Number of dice and Sides on each die, for example 2 and 6 for two standard dice.
- Choose What to find: the total of all the dice, or at least k dice showing a face.
- For a total, pick Comparison (Exactly, At least or At most) and type the Total. For a face, type the Face and At least k dice.
- Read Chance and As a fraction. The table under the result lists every total with its chance.
How the chance is calculated
Every outcome of rolling n dice with s sides is equally likely. The chance of an event is therefore the number of outcomes that match it, divided by all the outcomes, which is s to the power of n. The page counts the matching outcomes as whole numbers, so the fraction is exact before it is shown as a percentage.
Chance of a total = matching outcomes ÷ s^n. Chance that at least k dice show a face = Σ C(n, i) × (s − 1)^(n − i) ÷ s^n, for i from k to n.- For a total, the ways are built one die at a time. For two six-sided dice the totals 2 to 12 have 1, 2, 3, 4, 5, 6, 5, 4, 3, 2 and 1 ways.
- At least and at most add up the rows of the table from the total upwards or downwards.
- A face is any one value on a die. Every face of a fair die has the same chance, so the answer does not depend on which face you choose.
What this calculator does not cover
- Loaded or unfair dice: every face is taken to be equally likely.
- Exploding dice, rerolls and rules that keep or drop dice. The dice roller covers those notations.
- Contests against another roll, where the chance of winning depends on both players' rolls.
Worked example: two dice make a total of 7
Two six-sided dice make 6 times 6, which is 36 equally likely outcomes. A total of 7 can be made by 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1: six outcomes. The chance of exactly 7 is therefore 6 out of 36, which reduces to 1 in 6, or about 16.67%.
| Total | Ways to roll it | Chance |
|---|---|---|
| 6 | 5 | 13.889% |
| 7 | 6 | 16.667% |
| 8 | 5 | 13.889% |
Frequently asked questions
Why is a total of 7 with two dice more likely than a total of 2?
A total of 7 can be made in six different ways, while a total of 2 needs two 1s, which is one outcome out of 36. More ways to reach a total means a higher chance of it.
Does the order in which the dice land change the answer?
No. The dice are counted as separate dice, so a 2 on the first die and a 5 on the second is a different outcome from a 5 then a 2. Reading the dice in another order does not change the chance of any total.
How do I find the chance of at least one six in three rolls of one die?
Choose the face mode, set the number of dice to 3, the face to 6 and at least k dice to 1. The answer is 1 minus (5/6) cubed, which is 91 out of 216, or about 42.13%.
Why does the page assume the dice are fair?
The formulas give every face a chance of 1 in s. A loaded die changes those chances, and the page cannot know the weights of a die you did not describe, so it does not guess them.
What is the largest roll the page can handle?
The page accepts up to 20 dice with up to 100 sides each. A larger roll follows the same formulas, but its table of totals becomes too long to read on a phone.
Sources
Figures and text last checked on Tuesday, November 10, 2026.