Reviewed by CalcMulti Editorial Team·Last updated: ·← Probability Hub
This dice probability calculator computes the probability of rolling any exact sum or range of sums when rolling multiple dice. Supports standard die types: d4, d6, d8, d10, d12, and d20.
For a single d6, each outcome (1–6) has probability 1/6 ≈ 16.67%. With two d6, outcomes are not equally likely — there are 36 equally likely combinations, but only one way to roll a 2 (1+1) versus six ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
The expected value for one d6 is (1+2+3+4+5+6)/6 = 3.5. For two d6, E(sum) = 3.5 + 3.5 = 7 — the most probable sum when rolling 2d6. This is why 7 is the most common sum in craps.
Worked example — probability of rolling a sum of 8 with 2d6: ways to get 8 = {2+6, 3+5, 4+4, 5+3, 6+2} = 5 outcomes. Total combinations = 6² = 36. P(sum=8) = 5/36 ≈ 13.89%.
P(sum = k) = (ways to get k) / dⁿ
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.