Two Dice Probability Calculator
The probability of rolling a given total on two dice — exactly, at least or at most — with the full distribution behind it.
Two six-sided dice give 36 equally likely ordered outcomes.
How the two dice probability calculator works
Two six-sided dice give 36 equally likely ordered outcomes. The number of ways to make a total t is the count of pairs (a, b) with a + b = t, which rises to a peak at 7 (six ways) and falls symmetrically either side. The probability is that count ÷ 36.
This is why 7 is the pivot of craps and why the 6 and 8 spaces in backgammon matter: the distribution is triangular, not flat.
Formula: P(total = t) = ways(t) / (sides × sides)
Worked examples
| Inputs | P(total = target) | Note |
|---|---|---|
| Total of 7 on two d6 | 16.6667% | 6 ways in 36 — 16.67% |
| Snake eyes (total 2) | 2.7778% | 1 in 36 |
| Total of 12 on two d20 | 2.75% | 11 ways in 400 |
FAQFrequently asked questions
What is the probability of rolling a 7 with two dice?
6 in 36, which is 1 in 6 or about 16.67% — the most likely total.
Why is 7 the most common?
Because it has the most combinations: 1+6, 2+5, 3+4 and their reverses. Totals at the extremes have only one each.
What are the odds of snake eyes?
1 in 36, or 35 to 1 against.
Is the distribution flat?
No — it is triangular, peaking at 7. That shape is why board games built on two dice feel the way they do.
What about three dice?
The distribution becomes bell-shaped, and the peak splits between 10 and 11.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.