How to use the dice roller
- Enter the number of dice, from 1 to 100.
- Pick the type of die: d4, d6, d8, d10, d12, d20 or d100. Choose Custom for any die from 2 to 1,000 sides, such as a d3 or a d30.
- Enter a modifier if your game adds or subtracts a fixed number, such as +5 for an attack bonus or −2 for a penalty.
- The dice roll as soon as you change anything. To roll the same dice again, tick or untick Roll again.
- Read the total, each die, and the chance of rolling that total, that total or higher, and that total or lower.
How the dice are rolled and the odds worked out
Each die is rolled with your browser's cryptographic random number generator (crypto.getRandomValues), the same source used for passwords and security keys. Raw random numbers above the largest whole multiple of the number of sides are thrown away and drawn again, so no face comes up more often than another.
The odds are exact, not simulated. The calculator builds the full distribution of the total one die at a time:
Here n is the number of dice and s the number of sides. Adding one more die spreads every possible total across s new totals with equal weight, which is a convolution. The modifier just shifts every total by the same amount, so it never changes the odds of a roll, only the number you read.
Worked example
The default roll is 2d6 with no modifier, the dice used in many board games. Two dice have 6 × 6 = 36 equally likely outcomes:
- A total of 7 can come up 6 ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so P(7) = 6 ÷ 36 = 16.67%
- A total of 8 can come up 5 ways, so P(8) = 5 ÷ 36 = 13.89%
- 8 or higher covers 5 + 4 + 3 + 2 + 1 = 15 ways: 15 ÷ 36 = 41.67%
- The average total is 2 × (6 + 1) ÷ 2 = 7, and the range is 2 to 12
So if your dice show 3 and 5, the calculator reports a total of 8, a 13.89% chance of exactly 8, and a 41.67% chance of 8 or higher.
2d6 probability table
| Total | Ways | Chance | Total | Ways | Chance |
|---|---|---|---|---|---|
| 2 | 1 | 2.78% | 8 | 5 | 13.89% |
| 3 | 2 | 5.56% | 9 | 4 | 11.11% |
| 4 | 3 | 8.33% | 10 | 3 | 8.33% |
| 5 | 4 | 11.11% | 11 | 2 | 5.56% |
| 6 | 5 | 13.89% | 12 | 1 | 2.78% |
| 7 | 6 | 16.67% |
With more dice, totals bunch up around the average. With 3d6 the chance of exactly 10 or 11 is 12.5% each, while 3 or 18 is only 1 in 216. A single d20 is flat: every number from 1 to 20 has a 5% chance.
Common dice notation
Games write rolls as NdS+M: N dice with S sides, plus M. "3d8+2" means roll three eight-sided dice and add 2. "d%" or "d100" means a percentile roll from 1 to 100, often made with two d10s. Some games ask you to roll extra dice and drop the lowest, such as 4d6 drop lowest for character stats; roll 4d6 here and subtract the smallest die yourself.
Frequently asked questions
Are these online dice really random?
They use the cryptographic random number generator built into your browser, which is designed to be unpredictable. Every face is equally likely, and each roll is independent of the ones before it, just like a fair physical die.
What is the most likely total with two dice?
Seven. It can be made 6 ways out of 36, a 16.67% chance, more than any other total. Two and twelve are the least likely, with one way each (2.78%).
Does a modifier change the odds?
No. A modifier adds the same number to every possible total, so the shape of the distribution stays the same. The chance of rolling 8 on 2d6 equals the chance of 13 on 2d6+5.
How do I roll a d3 or a d30?
Choose Custom under Dice and enter the number of sides. Any whole number from 2 to 1,000 works, so you can also flip a coin with a d2.
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- Love Calculator — A just-for-fun compatibility score for two names. Same names, same score, every time.
- Permutation and Combination Calculator — nPr and nCr, with or without repetition, as exact whole numbers even when they run to thousands of digits.
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