Exact probabilities for any dice combination — no guessing, just math.
Configuration
Rolling 2d6 — possible sums 2 to 12 (11 outcomes)
Distribution Summary
Min Sum
2
Max Sum
12
Mean (Expected)
7.00
Std Deviation
2.42
Target Sum Lookup
Probability Distribution Chart
Click any bar to look up that sum. Height is proportional to probability.
Full Distribution Table
How it works: Probabilities are computed exactly using dynamic programming (DP convolution) — no simulation, no approximation. The number of ways to roll each sum is found by counting all combinations of die faces. Mean = N × (M+1)/2; Variance = N × (M²−1)/12.
The Dice Probability Calculator computes the exact probability of rolling any sum with N dice of M sides — whether you're playing D&D, board games, or designing a game mechanic. Using precise dynamic programming, it instantly generates the full probability distribution, cumulative odds, mean, and standard deviation for any combination like 2d6, 3d8, or 4d10.
Rolling a 7 on 2d6 has a probability of 6/36 = 16.67%. It is the most likely outcome because there are 6 ways to reach it: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). The calculator shows this automatically in the distribution table.
It uses dynamic programming (DP convolution) to count the exact number of ways to achieve each possible sum, then divides by the total number of outcomes (M^N). This gives exact results — not estimates — for any valid dice configuration up to 20 dice with 100 sides each.
'At least X' means P(roll ≥ X) — the chance of rolling that sum or higher. 'At most X' means P(roll ≤ X) — that sum or lower. These cumulative probabilities are useful in RPGs for target-number systems like 'roll 15 or higher on 3d6'.
The mean is N × (M+1)/2. For example, 2d6 has a mean of 7, and 1d20 has a mean of 10.5. The standard deviation is √(N × (M²−1)/12), which measures how spread out the results are around that average.