How the Dice Roller Works
The Dice Roller does what a real die does: it gives a whole number from 1 to the number of sides, and every number has the same chance. You can roll up to 20 dice at once, add or take away a number (a modifier), and drop the lowest dice, as many games ask you to do.
What you choose
- Number of dice: from 1 to 20.
- Sides per die: D2 (a coin), D4, D6, D8, D10, D12, D20 or D100.
- Drop the lowest: how many of the lowest dice to leave out of the total. Use 0 to keep all of them.
- Modifier: a number that is added to the total (or taken away, if it is negative).
The dice are written in the usual way: 2d6 means two dice with six sides, 1d20 + 5 means one twenty-sided die and add 5, and 4d6 drop the lowest 1 means roll four six-sided dice and add the highest three.
How the roll is made
each die = a random whole number from 1 to the sides total = sum of the dice that are kept + modifier
The random numbers come from the secure random generator of your browser, and not from a simple formula. A number that would make some results a little more likely than others is thrown away and drawn again, so 1 is as likely as the highest number. Each roll is separate: a die has no memory, and a 6 does not make another 6 more or less likely.
Example
| Roll | Dice | Total |
|---|---|---|
| 2d6 | 3 and 2 | 5 |
| 4d6, drop the lowest 1 | 5, 4, (1), 5 | 14 |
| 1d20 - 3 | 10 | 7 |
A die that is dropped is shown in brackets, and in gray in the chart of the calculator.
The average of each die
| Die | Numbers | Average |
|---|---|---|
| D2 | 1 to 2 | 1.5 |
| D4 | 1 to 4 | 2.5 |
| D6 | 1 to 6 | 3.5 |
| D8 | 1 to 8 | 4.5 |
| D10 | 1 to 10 | 5.5 |
| D12 | 1 to 12 | 6.5 |
| D20 | 1 to 20 | 10.5 |
| D100 | 1 to 100 | 50.5 |
The average of one die is (sides + 1) / 2. The average total of several dice is that number times the number of dice, plus the modifier. The calculator shows it when you do not drop any dice.
Chart: the chances for two six-sided dice
With two dice, the totals are not equally likely. There is only one way to make a 2 (1 and 1) but six ways to make a 7. Each block is about 0.4 percentage points, and the most likely total, 7, is green.
2 ███████ 1/36 = 2.8% 3 █████████████ 2/36 = 5.6% 4 ████████████████████ 3/36 = 8.3% 5 ███████████████████████████ 4/36 = 11.1% 6 █████████████████████████████████ 5/36 = 13.9% 7 ████████████████████████████████████████ 6/36 = 16.7% 8 █████████████████████████████████ 5/36 = 13.9% 9 ███████████████████████████ 4/36 = 11.1% 10 ████████████████████ 3/36 = 8.3% 11 █████████████ 2/36 = 5.6% 12 ███████ 1/36 = 2.8%
| Total | Ways (out of 36) | Chance |
|---|---|---|
| 2 | 1 | 2.8% |
| 3 | 2 | 5.6% |
| 4 | 3 | 8.3% |
| 5 | 4 | 11.1% |
| 6 | 5 | 13.9% |
| 7 | 6 | 16.7% |
| 8 | 5 | 13.9% |
| 9 | 4 | 11.1% |
| 10 | 3 | 8.3% |
| 11 | 2 | 5.6% |
| 12 | 1 | 2.8% |
The more dice you add, the more the totals bunch up around the average. This is the shape of a bell.
Chart: the chance to roll a number or more on a D20
Many role-playing games use a D20 and ask for a number or higher. Rolling two dice and taking the best (advantage) makes a high number much more likely. Each block is 2.5 percentage points.
>= 1 one d20 ████████████████████████████████████████ 100.0% best of 2 ████████████████████████████████████████ 100.0% >= 5 one d20 ████████████████████████████████ 80.0% best of 2 ██████████████████████████████████████ 96.0% >= 10 one d20 ██████████████████████ 55.0% best of 2 ████████████████████████████████ 79.8% >= 15 one d20 ████████████ 30.0% best of 2 ████████████████████ 51.0% >= 18 one d20 ██████ 15.0% best of 2 ███████████ 27.8% >= 20 one d20 ██ 5.0% best of 2 ████ 9.8%
Chart: 4d6 with the lowest die dropped
Dropping the lowest die moves the totals up. The average of 3d6 is 10.50, and the average of 4d6 with the lowest dropped is 12.24. Each block is about 0.32 percentage points, and the chances are exact.
3 3d6 █ 0.5% 4d6 drop █ 0.1% 6 3d6 ██████████████ 4.6% 4d6 drop █████ 1.6% 9 3d6 ███████████████████████████████████ 11.6% 4d6 drop █████████████████████ 7.0% 12 3d6 ███████████████████████████████████ 11.6% 4d6 drop ███████████████████████████████████████ 12.9% 15 3d6 ██████████████ 4.6% 4d6 drop ██████████████████████████████ 10.1% 18 3d6 █ 0.5% 4d6 drop █████ 1.6%
Tips
- Use the modifier for bonuses in a game, such as 1d20 + 5.
- Roll 4d6 and drop the lowest 1 to make the scores of a character in many role-playing games.
- Use a D2 for a coin. 1 is heads and 2 is tails, or the other way round.
- A D100 is used for a percentage roll: it gives 1 to 100.
What this roller does not include
- Dice that explode (roll again on the highest number), and rerolls of ones.
- Dice with sides other than the ones in the list, and dice with different numbers on the sides.
- Gambling. This roller is a tool for games and fun, and it is not meant for betting.
This tool is for games and general use. Its numbers are random, so it cannot predict the next roll.