Free dice roller calculator
Roll virtual dice in one click. Pick the die type — d4, d6, d8, d10, d12, d20, or d100 — choose how many to roll, and the dice roller shows each die, the sum, the expected (average) value, and the full odds of every total — a fresh, fair roll every time you press Roll.
On this page14 sections
| Sum | Ways | Probability |
|---|---|---|
| 4 | 3 | 8.3% |
| 5 | 4 | 11.1% |
| 6 | 5 | 13.9% |
| 7 | 6 | 16.7% |
| 8 | 5 | 13.9% |
| 9 | 4 | 11.1% |
Each die is rolled independently and uniformly — every face is equally likely. How fair are online dice?
Results are estimates. Consult a professional.
What is an online dice roller?
An online dice roller is a virtual replacement for physical dice: press one button and it generates a fair, random result for as many dice as you need. This dice roller handles every standard tabletop die — d4, d6, d8, d10, d12, d20, and d100 — rolls up to a dozen at once, and shows you each individual die alongside the running total. No app, no sign-up, and no lost dice down the back of the sofa.
It is built for two jobs at once. For board games and tabletop RPGs like Dungeons & Dragons it is a quick, honest stand-in for real dice. For anyone learning probability, it pairs the roll with the underlying odds — the expected value of each die and the full distribution of possible sums — so you can see the maths the dice are obeying, not just the result.
How to use the dice roller
Rolling is a three-step process, and the result appears the instant you press the button.
- Pick the die type. Choose d4, d6, d8, d10, d12, d20, or d100 — the standard polyhedral set. A d6 is the usual board-game cube; a d20 is the workhorse of Dungeons & Dragons.
- Set how many dice to roll. Slide the count from 1 up to 12. Two six-sided dice (2d6) is the classic board-game roll; six d6 is a common stat roll.
- Press Roll. The dice are generated randomly, each face is shown, and the sum is totalled for you. Press Roll again for a fresh, independent throw.
A worked example using the dice roller
Sam needs to move in a board game and the rules say to roll two six-sided dice (2d6) and move the total. Here is how the dice roller produces and explains that roll.
Step 1 — Choose the die type and count
Sam selects the d6 die type and sets the count to 2. The roller is now set up to throw two ordinary six-sided dice — written 2d6 in dice notation.
Step 2 — Press Roll and read each die
Sam presses Roll and the two dice come up 4 and 3. The roller shows each die separately so there is no ambiguity, then adds them: 4 + 3 = 7. Sam moves 7 spaces.
Step 3 — See the odds behind the result
Alongside the roll, the calculator shows the maths. The expected value of 2d6 is 7 — the average roll over the long run — so Sam's 7 is the single most likely total. There are 6 ways to make a 7 out of 36 possible outcomes, an exact probability of 6/36 ≈ 16.7%, more than any other sum.
Dice probability basics: expected value and odds
A fair die is the textbook example of a uniform distribution: every face is equally likely. On a six-sided die each number comes up with probability 1/6 ≈ 16.7%; on a twenty-sided die each face is 1/20 = 5%. From that one fact the rest of the dice maths follows.
Expected value — the average roll
The expected value is the long-run average of a die. For a single fair die it is simply the midpoint of its faces, (sides + 1) ÷ 2. Roll several dice and the expected values add up.
| Die type | Faces | Each face's odds | Expected value (1 die) |
|---|---|---|---|
| d4 | 4 | 1 in 4 (25%) | 2.5 |
| d6 | 6 | 1 in 6 (16.7%) | 3.5 |
| d8 | 8 | 1 in 8 (12.5%) | 4.5 |
| d10 | 10 | 1 in 10 (10%) | 5.5 |
| d12 | 12 | 1 in 12 (8.3%) | 6.5 |
| d20 | 20 | 1 in 20 (5%) | 10.5 |
| d100 | 100 | 1 in 100 (1%) | 50.5 |
Each face of a fair die is equally likely; the expected value is the midpoint, (sides + 1) ÷ 2.
The 2d6 sum distribution: why 7 is the magic number
Rolling a single die is uniform — every face equally likely — but the moment you add two dice together the totals stop being equal. Some sums can be made more ways than others. With two six-sided dice there are 36 equally likely outcomes (6 × 6), and they spread across the totals 2 through 12 in the famous triangular pattern below.
| Sum of 2d6 | Ways to roll it | Probability | Percent |
|---|---|---|---|
| 2 | 1 | 1/36 | 2.8% |
| 3 | 2 | 2/36 | 5.6% |
| 4 | 3 | 3/36 | 8.3% |
| 5 | 4 | 4/36 | 11.1% |
| 6 | 5 | 5/36 | 13.9% |
| 7 | 6 | 6/36 | 16.7% |
| 8 | 5 | 5/36 | 13.9% |
| 9 | 4 | 4/36 | 11.1% |
| 10 | 3 | 3/36 | 8.3% |
| 11 | 2 | 2/36 | 5.6% |
| 12 | 1 | 1/36 | 2.8% |
The 36 outcomes of 2d6 form a triangle: ways rise 1-2-3-4-5-6 up to the sum of 7, then fall back 5-4-3-2-1. The 11 ways sum to 36.
A 7 is the most likely total because it can be made six different ways — (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1) — while a 2 ("snake eyes") or a 12 ("boxcars") can each be made only one way. That is exactly why so many board games and the game of craps revolve around 7: it is not luck, it is the shape of the distribution.
Dice notation explained (3d6+2)
Tabletop games write dice rolls in a compact shorthand called dice notation. Once you can read it, any rulebook or character sheet makes sense at a glance. The general form is AdX+B.
| Notation | Means | Range | Average |
|---|---|---|---|
| 1d20 | Roll one twenty-sided die | 1–20 | 10.5 |
| 2d6 | Roll two six-sided dice, total them | 2–12 | 7 |
| 3d6 | Roll three six-sided dice, total them | 3–18 | 10.5 |
| 3d6+2 | Roll 3d6, then add 2 | 5–20 | 12.5 |
| 1d8+3 | Roll one d8, then add 3 | 4–11 | 7.5 |
| 4d6 drop lowest | Roll 4d6, keep the best three | 3–18 | ≈ 12.2 |
Common dice-notation examples. '3d6+2' means roll three six-sided dice and add 2 — averaging 10.5 + 2 = 12.5.
So a Dungeons & Dragons attack that does 3d6+2 damage means: roll three six-sided dice, total them (3 to 18), and add a flat 2 — a result somewhere from 5 to 20, averaging 12.5. To roll this here, set the die type to d6, the count to 3, press Roll, and add the modifier to the sum shown.
Are online dice rolls fair and truly random?
A die is fair when every face is equally likely and the next roll cannot be predicted from the last. By that definition a well-made digital roller is, if anything, fairer than a real die: a physical die is a flawed object — mass-produced dice carry tiny imperfections, and cheaper polyhedral dice can be slightly unbalanced and favour certain faces — whereas a software roll has no centre-of-gravity to lean on.
- Every roll is independent. The dice have no memory; previous results never change the odds of the next throw. This is the gambler's fallacy — a 7 is no more 'due' after a string of low rolls.
- Each face is equally likely. A fair d6 lands on each number 1/6 of the time over the long run; short streaks of repeats are normal and expected.
- Reproducible only by chance. Because the result is random, pressing Roll again gives a fresh, unrelated outcome — there is no hidden pattern to game.
Common dice types and where they are used
Beyond the everyday six-sided cube, tabletop gaming uses a whole set of polyhedral dice, each a regular solid (or near-regular) shape. The standard seven are below, with the geometric shape behind each and where you will meet it.
| Die | Shape | Faces | Typically used for |
|---|---|---|---|
| d4 | Tetrahedron | 4 | Small damage rolls, low-range randomisers |
| d6 | Cube | 6 | Board games, Yahtzee, craps, stat rolls |
| d8 | Octahedron | 8 | Weapon damage in RPGs |
| d10 | Pentagonal trapezohedron | 10 | Percentile rolls (paired), many RPG systems |
| d12 | Dodecahedron | 12 | Heavy-weapon damage, some RPG checks |
| d20 | Icosahedron | 20 | The core check die in Dungeons & Dragons |
| d100 | Two d10s / zocchihedron | 100 | Percentage rolls, loot and event tables |
The standard polyhedral set. A d100 is usually rolled as two ten-sided dice — one for the tens, one for the units.
Need a single number rather than a dice sum? The random number generator picks any integer in a range. To choose from a list of options at random, use the random pick from list tool, and for the odds of a draw-style game see the lottery odds calculator.
How this calculator works and sources
The roll runs entirely in your browser — nothing is sent anywhere. Each die is generated independently and uniformly when you press Roll, so every face is equally likely. The probability figures shown — expected values, the sum distribution, and the odds of any given total — are computed with exact integer maths (the 2d6 distribution is the standard 1-2-3-4-5-6-5-4-3-2-1 triangle over the 36 possible outcomes), not estimated from the rolls. Dice probability is standard, well-documented combinatorics.
Britannica — Probability theory: dice and the classical definition of probability.Frequently asked questions about the free dice roller calculator
About this dice roller
This dice roller runs entirely in your browser — nothing is sent to a server. Each die is generated independently and uniformly when you press Roll, so every face is equally likely, and the probability figures are computed with exact integer maths rather than estimated from the rolls.
Calculators Cloud offers 400+ free tools with no sign-up. The whole Everyday calculators shelf sits alongside this one, including the random number generator, random pick from list, and lottery odds tools. Or browse the full calculator directory.