With two dice, middle totals are more common because more combinations produce them; 7 is the most likely sum.
How to use the Dice Probability Calculator
- Target total (2–12)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Count the combinations that make the total and divide by the 36 possible outcomes.
What each result means
- P(exact total) = (6 – abs([Target total (2–12)] – 7))÷36×100
- Ways to roll it = 6 – abs([Target total (2–12)] – 7)
Example values
How the main result changes when Target total changes and everything else stays at the example values above:
| Target total (2–12) | P(exact total) (%) |
|---|---|
| 3.5 | 6.944 |
| 5.25 | 11.806 |
| 7 | 16.667 |
| 8.75 | 11.806 |
| 10.5 | 6.944 |
Formula
P(sum = s) = (6 − |s − 7|) ÷ 36 for 2 ≤ s ≤ 12Worked example
Inputs — Target total (2–12): 7.
Results — P(exact total) = 16.667 %; Ways to roll it = 6; P(total ≥ target) = 58.333 %.
Frequently asked questions
Why is 7 the most common total?
Six combinations make 7, more than any other sum.
What about three or more dice?
The distribution becomes more bell-shaped; it needs a convolution to compute.
What formula does the Dice Probability Calculator use?
P(sum = s) = (6 − |s − 7|) ÷ 36 for 2 ≤ s ≤ 12.