The **dice roller calculator** is a powerful tool designed to calculate the **probability** and **outcomes** of rolling one or more dice.

This tool is invaluable for a variety of applications, including

tabletop role-playing games,board games, and evenstatistical analysis.

## Dice Roller Chart

Dice Roll | 1D4 | 1D6 | 1D8 | 1D10 | 1D12 | 1D20 |
---|---|---|---|---|---|---|

1 | 25% | 16.67% | 12.5% | 10% | 8.33% | 5% |

2 | 25% | 16.67% | 12.5% | 10% | 8.33% | 5% |

3 | 25% | 16.67% | 12.5% | 10% | 8.33% | 5% |

4 | 25% | 16.67% | 12.5% | 10% | 8.33% | 5% |

5 | – | 16.67% | 12.5% | 10% | 8.33% | 5% |

6 | – | 16.67% | 12.5% | 10% | 8.33% | 5% |

7 | – | – | 12.5% | 10% | 8.33% | 5% |

8 | – | – | 12.5% | 10% | 8.33% | 5% |

9 | – | – | – | 10% | 8.33% | 5% |

10 | – | – | – | 10% | 8.33% | 5% |

11 | – | – | – | – | 8.33% | 5% |

12 | – | – | – | – | 8.33% | 5% |

13 | – | – | – | – | – | 5% |

14 | – | – | – | – | – | 5% |

15 | – | – | – | – | – | 5% |

16 | – | – | – | – | – | 5% |

17 | – | – | – | – | – | 5% |

18 | – | – | – | – | – | 5% |

19 | – | – | – | – | – | 5% |

20 | – | – | – | – | – | 5% |

This table shows the

probabilityof each possible outcome when rolling a single die of various types (D4, D6, D8, D10, D12, and D20).

## Dice Roller Calculation Formula

The formula for calculating the **probability** of a specific outcome when rolling one or more dice is:

**Probability = (Number of ways to get the outcome) / (Total number of possible outcomes)**

**If you roll a single D6 die, the probability of rolling a 3 is:**

**Probability = (Number of ways to get a 3) / (Total number of possible outcomes)**

**Probability = 1 / 6 = 16.67%**

This is because there is only one way to roll a 3 (the die shows the number 3), and there are a total of 6 possible outcomes (1, 2, 3, 4, 5, or 6).

**And if you roll two D6 dice, the probability of rolling a total of 7 is:**

**Probability = (Number of ways to get a 7) / (Total number of possible outcomes)**

**Probability = 6 / 36 = 16.67%**

This is because there are 6 ways to get a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), and there are 36 total possible outcomes (6 x 6) when rolling two D6 dice.

## How to Calculate Dice Roller?

To calculate the **probability distribution** and **expected value** of a dice roll, follow these steps:

**Find the number and type of dice:** Decide how many dice you want to roll and what type they are (D4, D6, D8, D10, D12, or D20).

**Calculate the total number of possible outcomes:** The total number of possible outcomes when rolling multiple dice is the product of the number of possible outcomes for each die. For example, if you roll two D6 dice, the total number of possible outcomes is 6 x 6 = 36.

**Identify the possible outcomes:** List all possible outcomes and their corresponding probabilities. For example, when rolling two D6 dice, the possible outcomes are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

**Calculate the probability of each outcome:** Use the formula

`Probability = (Number of ways to get the outcome) / (Total number of possible outcomes)`

to calculate the probability of each outcome.

**Determine the expected value:** The expected value is the average of all possible outcomes, weighted by their probabilities. To calculate the expected value, multiply each outcome by its probability, then sum the results.

The possible outcomes and their probabilities are:

Outcome | Probability |
---|---|

2 | 1/36 |

3 | 2/36 |

4 | 3/36 |

5 | 4/36 |

6 | 5/36 |

7 | 6/36 |

8 | 5/36 |

9 | 4/36 |

10 | 3/36 |

11 | 2/36 |

12 | 1/36 |

To calculate the expected value, we multiply each outcome by its probability and sum the results:

Expected Value = (2 × 1/36) + (3 × 2/36) + (4 × 3/36) + (5 × 4/36) + (6 × 5/36) + (7 × 6/36) + (8 × 5/36) + (9 × 4/36) + (10 × 3/36) + (11 × 2/36) + (12 × 1/36)Expected Value = 7

The expected value of rolling two D6 dice is **7**.

**Related Statistics Tools**