Dice Roller

Rolling virtual dice

1. Pick How many sides? from 3 to 40. A standard die is 6, the classic role-playing die is 20.
2. Pick How many dice to roll? from 1 to 10.
3. Press Roll Dice.

The first result line lists the number on each die in the order thrown. With two or more dice the tool adds a sum and a product line, which covers games that add the faces together and the less common ones that multiply them. A single die shows only its own number.

Common dice and their averages

A fair die with n faces numbered 1 to n has an average roll of (n + 1) ÷ 2, and k dice together average k × (n + 1) ÷ 2.

The odds behind a roll

On one fair die every face has probability 1 ÷ n. The chance that at least one of k dice shows a specific face is easiest to get from its opposite:

P(at least one specific face) = 1 − ((n − 1) ÷ n)^k

Example: the chance of at least one six when throwing four six-sided dice is 1 − (5 ÷ 6)⁴ = 1 − 0.4823 = 51.77%. With two dice there are 6 × 6 = 36 equally likely pairs, and the sums are not equally likely, because some sums can be made in more ways than others:

That is why 7 is the most common total with two dice and double six, at 1 ÷ 36, is as rare as double one.

How do we know the dice roller is random?

Each die is drawn from the cryptographically strong random generator built into your browser, with a fallback to the standard one if it is missing. A value in the range 1 to n is produced by discarding the few raw numbers that would make low faces slightly more likely, so every face has exactly the same probability. The dice are independent: five sixes in a row do not make a sixth any less likely, since the next throw is still 1 in 6.

The numbers are pseudo-random rather than the product of a physical throw, and nothing is stored or sent anywhere. If a roll matters to other people, such as a prize or a dispute, agree on the rules before you throw.

Online dice versus physical dice

Real dice are a pleasure to handle, but they are not perfect. Cheap dice can have uneven edges or slightly off-centre weight, and a lightly tossed die may not tumble enough to forget how it started. A virtual die has none of these issues and also gives you any number of faces, including unusual ones like a 3-sided or 30-sided die, and a total on the spot.

For deeper probability questions use the dice probability calculator, for plain numbers the random number generator, and to shuffle a list of options the list randomizer. For a yes-or-no coin toss, enter two lines in the random choice generator.