Dice Roller

What Is a Dice Roller?

A dice roller is a virtual set of dice. It picks a random number for each die, just as a real throw would, so you can play when the dice are lost or roll more dice than you own.

This one rolls ordinary six-sided dice, as in most board games, or non-conventional dice with any number of sides from 2 to 100, as in role-playing games. It shows the dice, their sum and product, and the chance of every sum.

Games write dice in a short code called dice notation: 2d6 means two six-sided dice added together, and 1d20 means one 20-sided die. The common dice have 4, 6, 8, 10, 12 and 20 sides, often called d4, d6, d8, d10, d12 and d20. A d100 gives a number from 1 to 100, and a d2 works like a coin flip.

How to Calculate Dice Probability

Each face of a fair die has the same chance, 1 in the number of sides. With several dice, count the ways to make a sum and divide by every possible outcome, which is the number of sides raised to the number of dice:

The number of ways for a sum k of n dice with s sides has an exact formula:

• n: the number of dice.
• s: the sides on each die.
• k: the sum of the dice.
• The brackets ( ) stacked like a fraction mean "choose": the number of ways to pick the bottom number of items from the top number.

You don't need the formula for a few dice: counting works. The average sum is easier still: n × (s + 1) ÷ 2. The product is all the dice multiplied together, which some games use instead of the sum.

Example

With two six-sided dice there are 6 × 6 = 36 outcomes. Here is how many ways make each sum:

• A 7 is the most likely sum: 6 ways out of 36, or 16.67%.
• A sum of 8 or more: 5 + 4 + 3 + 2 + 1 = 15 ways, so 15 ÷ 36 = 41.67%.
• The average: 2 × (6 + 1) ÷ 2 = 7.
• If you roll a 6 and a 1, the sum is 7 and the product is 6 × 1 = 6.

How to Use the Dice Roller

"I need to roll two dice for my board game, but they're lost." This calculator answers that.

The settings for this example are already filled in when the calculator opens, so you can roll straight away and then change them for your own game.

• Number of Dice: Enter 2, or drag the bar under the box. It can be from 1 to 100. Dice are added to the table or taken away as you change it.
• Sides per Die: Enter 6 for ordinary dice, or click the up and down arrows. For non-conventional dice, use any number from 2 to 100, such as 20 for a d20. Changing it puts dice with the new number of sides on the table.

Roll and Reset

Click Roll Dice to roll. The dice tumble for a moment and land on their numbers. If a box has a problem, such as letters, an empty box or 0 dice, a message pops up under that box instead. Each roll is random, so your numbers will differ; the chances don't.

• The dice: a picture of each die, at the top of the calculator. Six-sided dice show dots; other dice show their number, with a line under 6 and 9 as on real dice.
• Your Results: the Sum and Product, the dice added together and multiplied together. A very large product, from many dice, shows in powers of ten. Links under them jump to the chart and to your last rolls.
• Sum of 2d6: the headline number, with the chance of exactly that sum and of that sum or more, the average sum (7) and the lowest to highest sum (2 to 12).
• Chance of each sum: a chart of every sum's chance, with your sum in amber. With many possible sums it becomes a smooth curve.
• Your Last Rolls: after your second roll, a table of your last 10 rolls on this page.
• Share Results: a link that opens this page with the same dice and the same roll, so others can see what you rolled. Copy it, or share it on Facebook or X.

Click Reset to go back to two six-sided dice and clear your last rolls. It's greyed out while the boxes show 2 dice and 6 sides. The rolls use your browser's secure random numbers, with every face equally likely. Real dice can be slightly unbalanced, so their results may differ a little from these chances.