2 Dice Roller Calculator

Find the exact probability of any total when rolling two standard six-sided dice — the chance of hitting, exceeding, or falling below a target sum out of 36 equally likely outcomes.

Quick Facts

Method
Exact count over 36 equally likely (die1, die2) outcomes
Probability = favorable outcomes ÷ 36. The sum distribution peaks at 7 and is symmetric.

Your Results

Calculated
Probability
-
Chance of the condition
As a fraction
-
Favorable ÷ 36
Odds against
-
Against : for
Favorable outcomes
-
Out of 36 total

Ready

Choose a target sum and condition, then calculate.

Understanding the 2 Dice Roller

When you roll two standard six-sided dice, each die is independent and shows a number from 1 to 6 with equal probability. Because die A has 6 faces and die B has 6 faces, there are 6 × 6 = 36 equally likely ordered outcomes — from (1,1) up to (6,6). Every probability on this page is just the count of outcomes that satisfy your condition, divided by 36.

How the sum is distributed

The two dice can total anywhere from 2 (a pair of ones) to 12 (a pair of sixes). The totals are not equally likely, though: a 7 can be built six different ways, while a 2 or a 12 can each be built only one way. This gives the classic triangular ("tent") distribution that peaks at 7 and is perfectly symmetric around it.

SumWays to make itProbabilityPercent
211/362.78%
321/185.56%
431/128.33%
541/911.11%
655/3613.89%
761/616.67%
855/3613.89%
941/911.11%
1031/128.33%
1121/185.56%
1211/362.78%

The 11 counts add up to 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36, confirming every outcome is accounted for exactly once.

The formula

  • Exact sum: P(sum = s) = ways(s) / 36, where ways(s) counts the (die A, die B) pairs that add to s. For s from 2 to 7 the count rises as 6 − |7 − s|; from 7 to 12 it falls by the same rule.
  • At least / at most: P(sum ≥ s) and P(sum ≤ s) add up the individual ways across all qualifying totals, then divide by 36. For example P(sum ≥ 10) = (3 + 2 + 1)/36 = 6/36 = 1/6.
  • Odds against: if f outcomes are favorable, the odds against are (36 − f) : f, reduced to lowest terms. A 7 has odds of 30 : 6 = 5 : 1 against.

Key reference points

  • Most likely total: 7, at 6/36 ≈ 16.67%.
  • Rarest totals: 2 and 12, each at 1/36 ≈ 2.78%.
  • Expected value: the mean sum is 7 (each die averages 3.5, and 3.5 + 3.5 = 7).
  • Doubles: six of the 36 outcomes are doubles (1-1 through 6-6), so any double is 6/36 = 1/6 ≈ 16.67%.
  • Beating a 7: P(sum > 7) = P(sum < 7) = 15/36 ≈ 41.67% by symmetry, leaving 6/36 for exactly 7.

Frequently Asked Questions

What is the most likely sum when rolling two dice?
Seven. It can be made six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 equally likely outcomes, so its probability is 6/36 = 1/6 ≈ 16.67%. The distribution is symmetric, peaking at 7 and tapering off evenly toward 2 and 12.
What are the odds of rolling doubles?
There are six ways to roll matching numbers — (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) — out of 36 outcomes, giving 6/36 = 1/6 ≈ 16.67%. Any one specific double, such as double sixes, is 1/36 ≈ 2.78%.
Why isn't every total from 2 to 12 equally likely?
Because each total can be reached by a different number of dice combinations. A 7 has six pairings, but a 2 requires both dice to show 1, which happens just one way. Counting the ordered (die A, die B) pairs — not the possible totals — is what makes the probabilities correct.
Does the order of the dice matter?
For counting outcomes it does: (2,5) and (5,2) are two distinct rolls, which is why the total of 36 is used. But for the sum they give the same result (7), so both are simply counted among the favorable outcomes for that total.

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