Dice probability calculator
Enter how many dice you roll, how many sides they have and the total you need. You get the chance of rolling exactly that total, at least it and at most it, along with the number of ways, the average and a chart of every possible sum.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the number of dice and the number of sides.
- Enter the target total.
- Read the chance of exactly that total and the at-least and at-most chances; the chart shows every sum.
How it works
With one die every face has chance 1/M. Each further die spreads the distribution: the new chance of a total s is (P(s − 1) + … + P(s − M)) / M. A running window sum makes each die cost one pass over the table. The number of ways is shown while Mᴺ is small enough for exact whole numbers.
Worked example
Three six-sided dice, target 10: there are 27 ways out of 6³ = 216, so P(sum = 10) = 27 / 216 = 0.125. With two dice, P(sum ≥ 10) = (3 + 2 + 1) / 36 = 1/6.
Tips
- For “at least one six” in several dice, use the probability calculator’s “At least one success in n trials” mode: 1 − (5/6)ᴺ.
- To actually roll, open the dice roller.
Frequently asked questions
What is the chance of rolling 7 with two dice?
6 in 36, or 1/6 ≈ 0.1667: the pairs 1-6, 2-5, 3-4, 4-3, 5-2 and 6-1 give 7 out of 6 × 6 = 36 equally likely outcomes. 7 is the most likely sum with two six-sided dice.
How is the probability of a sum calculated?
The distribution is built one die at a time. Adding a die with M sides, the chance of a new total s is the average of the old chances of s − 1, s − 2, …, s − M. This gives the exact distribution for any number of dice without listing every roll.
What does “at least” mean here?
P(sum ≥ target) adds the chances of the target and every higher total. For a d20 save of 15 or more, that is 6 of 20 faces: 0.3.
Why does the curve look like a bell with many dice?
Sums of many independent dice approach a normal distribution (the central limit theorem). The mean is N(M + 1)/2 and the variance N(M² − 1)/12; for 4d6 that is 14 and a standard deviation of about 3.42.