Dice probability calculator.

Answer

Probability = ways to reach the total / (sides ^ dice). For 3d6 + 2, the chance of a total of at least 15 is 25.93% (1 in 3.9); the average total is 12.50 and the standard deviation is 2.96. Two six-sided dice total exactly 7 with probability 6/36, 16.67%.

Worked example

Roll 3d6 and add 2, and you want 15 or more. The dice must total at least 13, because 13 + 2 = 15. Of the 216 equally likely outcomes of three six-sided dice, 56 total 13 or higher, so the chance is 56 / 216 = 25.93%.

How it works

Counting ways. Every die is fair and independent, so each of the sides ^ dice ordered outcomes is equally likely. The calculator builds the number of ways to reach each total one die at a time and divides by that grand total. Four six-sided dice, for example, have 1,296 outcomes and 146 of them total exactly 14.

Mean and spread. One die with s sides averages (s + 1) / 2. The mean total is dice x (s + 1) / 2 plus the modifier, and the standard deviation is the square root of dice x (s^2 - 1) / 12. The table lists the totals nearest the mean when there are more than 121 possible totals.

Limits. Up to 50 dice with up to 100 sides. Dropping or keeping dice (such as 4d6 drop lowest) is a different calculation, covered by the 4d6 drop lowest tool.

Sources and basis (opened 2026-10-08): arithmetic on fair dice, no outside data. Exact counts are checked against full enumeration of every outcome in the test suite.

FAQ

What is the probability of rolling a 7 with two dice?

16.67%. Six of the 36 equally likely outcomes of two six-sided dice total 7, so it is the most likely total.

Why are middle totals more likely than extreme totals?

There are more combinations of faces that make a middle total. With two six-sided dice there is only one way to roll 2 (1 and 1) but six ways to roll 7.

Does a modifier change the odds?

It shifts every total by the same amount, so a +2 modifier makes a target of 15 equivalent to a dice total of 13. The shape of the distribution does not change.

How do I find the chance of rolling at least a number?

Pick the At least option and enter the target. The calculator adds up the probability of every total from the target upward.

Can it handle keeping the highest dice?

No. This tool sums every die. For rolls that drop the lowest die, use the 4d6 drop lowest calculator.