Find the chance of rolling a chosen face exactly k times, or at least k times, on n fair dice.
| P(exactly k) | – |
| P(at least k) | – |
Use this calculator for fair, independent dice when you care about how often a particular face appears, not about the sum of the dice. Two six-siders looking for sixes, a D20, or a handful of custom dice all fit this binomial model.
Each die is a trial with success probability p = 1 / sides. Then P(exactly k) = C(n, k) p^k (1 − p)^{n − k} and P(at least k) is the sum of that PMF from k through n. Two six-sided dice and k = 1 give P(exactly one six) ≈ 0.2778 and P(at least one six) ≈ 0.3056.
Dice are assumed fair and independent. This is not the distribution of the total pips. k cannot exceed the number of dice.
Dice (n): How many dice you roll.
Sides: Faces on each die. 6 is a standard die, 20 is a D20.
Count (k): How many times you want the chosen face.
P(exactly k): Probability of exactly k of that face.
P(at least k): Probability of k or more of that face.
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