What this calculator does
Rolling two dice and asking about a single total is a different question from rolling one die and asking about one number. This dice probability calculator handles the multi-dice case: pick how many dice, what size, a target sum, and whether you want that sum exactly, or that sum or higher, or that sum or lower, and it works through every possible combination to give an exact answer.
The classic example is two six-sided dice, where 7 is the most common total because six different pairs make it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while 2 and 12 only have one combination each. This calculator generalises that same logic to any number of dice, any die size, and lays out the full dice probability chart so the pattern is visible at a glance rather than just the single number you asked for.
The formula
The calculator enumerates every combination the chosen dice can produce, one die at a time, building up a count of how many combinations land on each possible sum. Dividing the count for a given sum by the total number of combinations (die size raised to the power of the number of dice) gives the exact probability, with no simulation or approximation involved.
| Term | Meaning |
|---|---|
| Sum | The total of all the dice rolled together, ranging from the number of dice (all 1s) to dice × sides (all maximums). |
| Ways to make it | The count of distinct combinations of individual die results that add up to that sum. |
| Probability | Ways to make that sum, divided by the total number of possible combinations across all the dice. |
The inputs explained
| Field | What to enter |
|---|---|
| Number of dice | How many dice are being rolled together, from 1 to 4. |
| Die size | The number of faces on each die. |
| Target sum | The total you are interested in. |
| Probability of rolling a sum that is | Whether you want that exact total, that total or better, or that total or worse. |
When to use it
Board and tabletop games
Many games are built around two-dice sums, and knowing that 7 comes up nearly six times as often as 2 or 12 changes how a player should weigh bets or space movements around the board.
Checking a dice probability chart by hand
Rather than trusting a chart copied from somewhere else, this recomputes the exact distribution for the specific dice count and size in front of you, including sizes other than the standard d6.
Designing a game mechanic
Anyone building a system around multiple dice can check the actual shape of the sum distribution before committing to a target number that is meant to be rare, common or roughly even odds.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Two dice probability table: every sum from 2 to 12
The full two dice probability table for the standard 2d6 case, the most commonly asked-about version of this question.
| Sum | Probability | Favourable outcomes |
|---|---|---|
| 2 | 2.78% | 1 |
| 3 | 5.56% | 2 |
| 4 | 8.33% | 3 |
| 5 | 11.1% | 4 |
| 6 | 13.9% | 5 |
| 7 | 16.7% | 6 |
| 8 | 13.9% | 5 |
| 9 | 11.1% | 4 |
| 10 | 8.33% | 3 |
| 11 | 5.56% | 2 |
| 12 | 2.78% | 1 |
How the odds of rolling a sum of 4 exactly change with more dice
The same target sum of 4, as the number of six-sided dice being rolled increases from one to four.
Questions
Why is 7 the most common result on two six-sided dice?
There are 6 different pairs of rolls that add up to 7 (1+6 through 6+1), more than for any other total, out of 36 equally likely pairs in total. No other sum on 2d6 has more than 5 combinations.
What is the two dice probability table for 2d6?
Sums of 2 and 12 each have 1 combination (2.78%), 3 and 11 have 2 (5.56%), 4 and 10 have 3 (8.33%), 5 and 9 have 4 (11.1%), 6 and 8 have 5 (13.9%), and 7 has 6 (16.7%), out of 36 total combinations.
How is this different from a single-die probability calculator?
A single-die calculator answers questions about one die landing on or above a given face. This one answers questions about the combined total of two or more dice rolled together, which follows a completely different distribution because some totals can be reached in more ways than others.
Does this work for dice other than six-sided?
Yes. Any of the standard die sizes can be chosen, and the calculator enumerates the exact combinations for that size rather than assuming a six-sided die.
For the probability of a single die landing on or above one particular face, see the dice roll probability calculator. For other probability questions with a fixed set of outcomes, the interquartile range calculator covers a different corner of descriptive statistics.