Interactive simulator
Dice roller
Roll any combination of polyhedral dice.
Total-
Individual rolls-
Average-
About this dice roller
This dice roller handles any combination of polyhedral dice used in tabletop role-playing games and board games: d4, d6, d8, d10, d12, d20, and the percentile d100. Pick how many dice and how many sides, roll, and the tool reports each individual die, the total, and the average. Every die is rolled with crypto.getRandomValues, the browser's cryptographically secure random source, so the results are unbiased and unpredictable, unlike a worn physical die that can favour one face.
The shorthand the hobby uses is dice notation, written NdM+X: N dice, each with M sides, plus an optional modifier X. So 1d20 is a single twenty-sided roll, 4d6 is four six-siders summed, and 2d8+3 is two eight-siders plus three. Dungeons and Dragons, Pathfinder, and most modern systems are built on this notation, which is why a digital roller that speaks it is useful at the table and online.
How it works
A single die of M sides is a uniform distribution: every face from 1 to M is equally likely. When you sum several dice the distribution changes shape; the total clusters around the mean and the extremes become rare. The key figures:
single die (dM): each face = 1/M chance, mean = (M + 1) / 2
N dice (NdM): min = N, max = N x M
mean total = N x (M + 1) / 2
3d6 example: mean = 3 x 3.5 = 10.5, range 3 to 18
percentile d100: roll d100 directly, or d10 (tens) + d10 (ones)
- One die is flat: on a d20 every number 1 to 20 is equally likely (5 percent each).
- Many dice are bell-shaped: summing dice (3d6) makes middle totals far more common than the extremes.
- Modifiers shift, not spread: +3 moves the whole range up by 3 without changing the odds of each relative outcome.
Worked example
A D&D character rolls 2d6+3 for a longsword damage roll. What can they expect?
- Dice portion: 2d6 ranges from 2 (two 1s) to 12 (two 6s).
- Mean of 2d6: 2 x (6 + 1) / 2 = 2 x 3.5 = 7.
- Add the modifier: 7 + 3 = 10 average damage; the range becomes 5 to 15.
- Most common single total: on 2d6 the peak is 7 (six ways out of 36), so 7 + 3 = 10 is the single likeliest result.
Result: A 2d6+3 attack averages 10 damage, can never roll below 5, and peaks at 10 because the bell-shaped sum of two dice favours the middle. Rolling boxcars (double 6) for 15 happens only 1 time in 36.
Dice reference
| Die | Range | Average roll | Common use |
|---|---|---|---|
| d4 | 1 to 4 | 2.5 | Dagger damage, minor effects |
| d6 | 1 to 6 | 3.5 | Shortsword, board games, 3d6 stats |
| d8 | 1 to 8 | 4.5 | Longsword, many spells |
| d10 | 1 to 10 | 5.5 | Percentile tens, heavy weapons |
| d12 | 1 to 12 | 6.5 | Greataxe, barbarian hit dice |
| d20 | 1 to 20 | 10.5 | Attack rolls, ability checks, saves |
| d100 | 1 to 100 | 50.5 | Percentile rolls, random tables |
A brief history of dice
Dice are among the oldest gaming tools known. Excavations of the Burnt City in southeastern Iran turned up a set dated to roughly 2800 to 2500 BCE, and cubic dice with the modern 1-to-6 pip layout were widespread in the ancient world; the Romans were avid players, using both six-sided tesserae and four-sided tali made from animal knucklebones. The convention that opposite faces of a standard die sum to seven (1 opposite 6, 2 opposite 5, 3 opposite 4) was already common in antiquity and is still used today.
The full polyhedral set, the d4, d8, d10, d12, and d20 alongside the familiar d6, entered popular use with tabletop role-playing games in the 1970s, when Dungeons and Dragons adopted the five Platonic solids plus the ten-sided die for percentile rolls. Those shapes were chosen because each is a fair die: every face is geometrically identical, so a well-made example is equally likely to land on any side. The study of dice odds also helped found probability theory itself, in the seventeenth-century correspondence between Blaise Pascal and Pierre de Fermat over a gambling problem.
Probability of common rolls
For summed dice the totals follow a bell-shaped distribution. The classic case is 3d6, where each total from 3 to 18 has a fixed number of combinations out of 216:
| 3d6 total | Ways to roll it | Probability |
|---|---|---|
| 3 or 18 | 1 | 0.46% |
| 4 or 17 | 3 | 1.39% |
| 7 or 14 | 15 | 6.94% |
| 10 or 11 | 27 | 12.50% |
The peak at 10 and 11 is 27 times as likely as the extremes of 3 or 18, which is why ability scores rolled on 3d6 cluster near the middle and why dropping the lowest of 4d6 shifts the average upward.
Common pitfalls
- Assuming 3d6 and 1d18 are the same. Both span a wide range, but 3d6 is bell-shaped (10 and 11 are common, 3 and 18 are rare) while a flat d18 would make every value equally likely.
- Forgetting the minimum is N, not 1. The lowest 4d6 can roll is 4, because each of the four dice shows at least a 1.
- Misreading percentile dice. Two d10s give 1 to 100, where a "00" and a "0" usually read as 100, not 0. Set the convention before you roll.
- Applying a modifier per die. In
2d6+3the +3 is added once to the total, not 3 to each die. Per-die bonuses are written differently. - Expecting "average" on every roll. The mean of 1d20 is 10.5, but you will never roll 10.5; single dice are streaky by nature.
- Trusting a chipped physical die. Worn or unbalanced dice drift from fair. A digital roller stays perfectly uniform across thousands of rolls.
Related tools
Frequently asked questions
What does dice notation like 4d6+2 mean?
It follows the pattern NdM+X: roll N dice that each have M sides, then add the modifier X to the total. So 4d6+2 means roll four six-sided dice, sum them, and add 2. The result ranges from 6 to 26 with an average of 16.
What is the average roll of a d20?
10.5. A fair d20 has each face from 1 to 20 equally likely, so the mean is (1 + 20) / 2 = 10.5. You can never roll exactly 10.5 on one die, but over many rolls the average settles near it.
Why is 3d6 more likely to land on 10 or 11 than on 3?
Because summing dice produces a bell-shaped distribution. There is only one way to roll a 3 (1+1+1) but 27 different ways to roll a 10 or 11 out of 216 combinations, so the middle totals are far more common than the extremes.
Are the rolls genuinely random?
Yes. The roller uses crypto.getRandomValues, the browser's cryptographically secure generator, rather than the predictable Math.random. Each face is equally likely with no bias, which is actually fairer than many worn or unbalanced physical dice.
How do percentile dice (d100) work?
A d100 produces a number from 1 to 100. Physically it is usually rolled as two ten-sided dice, one read as the tens digit and one as the ones; a result of "00" plus "0" conventionally counts as 100. This tool can roll a d100 directly.