How the probability is calculated
Two dice produce 36 equally likely ordered outcomes (6 × 6). The number of those outcomes that add up to a given sum follows a simple triangular pattern peaking at 7, so the probability is just that count divided by 36.
- sum — the target total, 2 through 12
- favorable — number of (die1, die2) pairs that add to sum
- 36 — total possible outcomes (6 × 6)
More detail
Why 7 is the most likely sum
7 can be made 6 different ways — (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — more than any other total, giving it a 6/36 ≈ 16.7% chance. Sums further from 7 have fewer ordered pairs: only one way each to make 2 (1,1) or 12 (6,6), for a 1/36 ≈ 2.8% chance.
Why order matters in the count
Rolling a 3 then a 4 and rolling a 4 then a 3 are counted as two separate outcomes, not one — that's why the sample space is 36, not 21. This is the standard convention for independent dice and matches how the formula above is derived.
Quick check. The favorable-outcome counts always mirror around 7: sum 8 has the same probability as sum 6, sum 9 the same as sum 5, and so on — because |sum − 7| is the same on both sides.
Frequently asked questions
What's the probability of rolling a sum of 7 with two dice?
6/36 = 1/6 ≈ 16.7%, the highest of any total. There are 6 ordered pairs that sum to 7 — (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — more than any other sum from 2 to 12. Enter 7 above to see this computed.
Why is the total sample space 36 and not 21?
Each die roll is independent and ordered, so (2,5) and (5,2) count as two different outcomes even though they share the same sum — giving 6 × 6 = 36 total outcomes, not the 21 you'd get by treating unordered pairs as one.
What's the probability of rolling a 2 or a 12 (snake eyes or boxcars)?
Each has only 1 favorable outcome out of 36 — (1,1) for a sum of 2, (6,6) for a sum of 12 — so each has a 1/36 ≈ 2.8% probability, the lowest of any sum. Enter 2 or 12 above to confirm.
Is this the same for a sum outside 2–12?
No — with two six-sided dice the minimum possible sum is 2 (1+1) and the maximum is 12 (6+6), so any target outside that range is impossible and this calculator shows “—”.