Everyday calculator

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.

InputsLive
Die type
How many dice2d6
How the odds are calculated
Each face of a fair die is equally likely. The average (expected value) of one die is:expected value = (sides + 1) / 2
  • One d6 averages 3.5; the average of N dice is N × that.
  • Adding dice clusters the totals around the average — on 2d6 a sum of 7 is the most likely.
  • The roll itself is random; the probabilities are exact maths.
Result
Roll 2d6
2
Press Roll 2d6 to throw the dice. The expected (average) total is 7.
Each die
11
Sum2
Dice2d6
Expected value7
Range2–12
Most likely totals for 2d6
SumWaysProbability
438.3%
5411.1%
6513.9%
7616.7%
8513.9%
9411.1%

Each die is rolled independently and uniformly — every face is equally likely. How fair are online dice?

Results are estimates. Consult a professional.

Overview

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.

A die is one numbered cube or polyhedron; 'dice' is the plural. A d6 is the everyday six-sided cube.
A die with N faces. d6 is six-sided, d20 is twenty-sided. The 'd' stands for 'die'.
A single random outcome. One die roll returns one face; rolling N dice returns N faces and their sum.
The total of all the dice in one roll — the figure most board games and RPG checks actually use.
Method

How to use the dice roller

Rolling is a three-step process, and the result appears the instant you press the button.

  1. 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.
  2. 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.
  3. 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.
Every roll is independent — the dice have no memory. A run of low numbers does not make a high number 'due' on the next throw. Each face is equally likely every single time.
Worked example

A worked example using the dice roller

Example: rolling 2d6 for a board game

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.

Roll: 4 + 3 = 7
Two d6 came up 4 and 3 for a sum of 7 — the most likely 2d6 total, with odds of 6/36 (about 16.7%) and an expected value of 7.
The maths

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.

expected value of one die = (sides + 1) / 2
1d6 → (6 + 1) / 2 = 3.5
1d20 → (20 + 1) / 2 = 10.5
expected value of N dice = N × (sides + 1) / 2
2d6 → 2 × 3.5 = 7
Die typeFacesEach face's oddsExpected value (1 die)
d441 in 4 (25%)2.5
d661 in 6 (16.7%)3.5
d881 in 8 (12.5%)4.5
d10101 in 10 (10%)5.5
d12121 in 12 (8.3%)6.5
d20201 in 20 (5%)10.5
d1001001 in 100 (1%)50.5

Each face of a fair die is equally likely; the expected value is the midpoint, (sides + 1) ÷ 2.

Distribution

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 2d6Ways to roll itProbabilityPercent
211/362.8%
322/365.6%
433/368.3%
544/3611.1%
655/3613.9%
766/3616.7%
855/3613.9%
944/3611.1%
1033/368.3%
1122/365.6%
1211/362.8%

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.

Add more dice and the triangle becomes a smooth bell curve clustered around the average. With 3d6 the most likely totals are 10 and 11 (each 27 ways out of 216), and the extremes — a 3 or an 18 — get rarer still, at 1 in 216 each.
Tabletop

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.

A d X + B
A = how many dice to roll
X = the number of sides on each die
B = a fixed modifier added to (or subtracted from) the total
NotationMeansRangeAverage
1d20Roll one twenty-sided die1–2010.5
2d6Roll two six-sided dice, total them2–127
3d6Roll three six-sided dice, total them3–1810.5
3d6+2Roll 3d6, then add 25–2012.5
1d8+3Roll one d8, then add 34–117.5
4d6 drop lowestRoll 4d6, keep the best three3–18≈ 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.

Randomness

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.
Want to test a physical die's fairness? The classic salt-water float test: dissolve enough salt in water to float the die, then flick it. If the same numbers keep landing face-up, the die is weighted and not fair.
Reference

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.

DieShapeFacesTypically used for
d4Tetrahedron4Small damage rolls, low-range randomisers
d6Cube6Board games, Yahtzee, craps, stat rolls
d8Octahedron8Weapon damage in RPGs
d10Pentagonal trapezohedron10Percentile rolls (paired), many RPG systems
d12Dodecahedron12Heavy-weapon damage, some RPG checks
d20Icosahedron20The core check die in Dungeons & Dragons
d100Two d10s / zocchihedron100Percentage 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.

Methodology

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.
Questions

Frequently asked questions about the free dice roller calculator

A dice roller calculator is a free online tool that helps you roll virtual dice online — d4, d6, d8, d10, d12, d20, and d100 — up to 12 at once, with each die, the sum, expected value, and the full sum-probability distribution. Each die is rolled independently and uniformly; every face is equally likely. The maths (expected value, sum distribution) is exact. It runs entirely in your browser with instant results and no sign-up.
Get a container that fits the die, fill it with water, then add salt until the die floats. Flick the die and note which side faces up. If the same numbers keep landing face-up, the die is weighted and not perfectly fair.
Yes — a digital die is typically truly random, whereas a real die, being a flawed physical object, tends to show small bias because manufacturers cannot make perfectly uniform dice. Each online roll is independent and every face is equally likely.
There are 6 ways to make a 7 out of 36 possible outcomes on 2d6 — (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — so the probability is 6/36 ≈ 16.7%. That makes 7 the most likely total.
A single fair d6 averages 3.5 — the midpoint of 1 through 6, a value it can never actually roll. Two d6 average 7. In general the average of one die is (sides + 1) ÷ 2, and the average of N dice is N times that.
No. Each roll is independent — the dice have no memory. A run of low numbers does not make a high number 'due'; every face is equally likely on every throw.
About

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.

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