Online Dice Roller

Pick your dice, roll, and see how likely that total really was

This roller handles seven kinds of dice, D4, D6, D8, D10, D12, D20 and D100, in any mix up to 30 dice. Click the tray and the dice tumble around inside it, then settle on the total and the face of each die. It covers everything from two six-sided dice for a board game to a tabletop roleplaying check like "1d20 + 5" where a modifier is added to the roll.

Once a total comes up, the tool also works out how often it turns up. If two D6 show 9, the chance of rolling 9 or more is 27.8%, and the chance of exactly 9 is 11.1% (4 of 36 outcomes). These figures are not simulation estimates: they come from counting every combination of faces. The probability bars below fill with your own results as dark bars, so the more you roll, the closer your results drift toward the exact shape.

When a screen beats a handful of real dice

Dice are used for games and decisions because nobody can pick the outcome. A virtual die keeps that property and removes a few everyday hassles.

• Playing over a video call: when a tabletop roleplaying group or a board-game night moves online, everyone can open the same tray, and the rolled faces and total are easy to read out loud.
• Teaching a class: a teacher can share the screen, roll 2d6 a thousand times and let students watch the bars settle toward the exact probabilities, with no box of dice to pass around.
• Mixed dice: a roll such as "2d6 + 1d8 + 3" means reading each die and adding by hand. Here the faces by type and the total appear at once.
• Knowing the odds first: enter a target and you see, before you roll, how likely you are to reach it.

How to use it

1. Choose a similar roll from the examples, or set the number of each die with the − and + buttons. You can also type an expression such as "2d6 + 3" in the expression box.
2. If you need a modifier, set it in the ± row. The total is the sum of the faces plus the modifier.
3. For a check, enter a target and choose "or higher" or "or lower". D20 checks usually use "or higher" and D100 checks usually use "or lower".
4. Click the tray or Roll. For experiments, "Many times" rolls 10 to 10,000 times in one go.
5. Hover over a bar, or select it and use the arrow keys, to read the chance of that total and how often your rolls landed there. At a table, full screen shows just the tray, and the space bar rolls.

The seven dice and the average of a single die

On one die every face is equally likely. With n faces, each face comes up with probability 1/n, and the average (expected value) is (n + 1) ÷ 2. The standard deviation describes how widely the faces spread around that average, and it grows with the number of faces.

The D4, D6, D8, D12 and D20 are the five Platonic solids, with every face the same regular polygon. The D10 has kite-shaped faces, so it is not a Platonic solid, but its faces are all identical and it rolls fairly. Some physical D10s are numbered 0 to 9, with a 0 in place of the 10; this tool reads them as 1 to 10. With several dice, the average total is the sum of the individual averages, so 2D6 averages 7 and "2d6 + 1d20 + 3" averages 7 + 10.5 + 3 = 20.5.

With two D6, a total of 7 comes up most often

Two D6 give 6 × 6 = 36 combinations of faces, all equally likely. A total of 7 can be made six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), more than any other, while 2 and 12 can each be made only one way. That is why the totals of 2D6 form a triangle that peaks in the middle.

An average of 7 does not make "7 or more" a coin flip. Because 7 itself is the most common total at 16.7%, 7 or more is 58.3%, and you have to go to 8 or more to drop below half, at 41.7%. A single D12 and 2D6 may look alike because both span a similar range, but they behave very differently. The D12 can show 1 and every value has the same 8.3% chance, while 2D6 can never show 1 and a 7 comes up six times as often as a 2 or a 12.

The more dice you add, the more totals bunch in the middle

Each extra die pulls the distribution of the total toward a bell shape: low at both ends and high in the middle. Compare 1D20 with 3D6, which span a similar range. Every face of a D20 has a flat 5.0% chance, but with 3D6 the totals 10 and 11 are the most likely at 12.5% each, while 3 and 18 are just one outcome out of 216 (0.5%).

So a 16 or more shows up about one time in four with 1D20, but less than one time in twenty with 3D6. This is why a game that wants swingy results uses a single die, and one that wants steady results around the average sums several. A modifier does not change the shape of the distribution; it only slides the whole set of bars sideways.

Target checks: D20 rolls high, D100 rolls low

The System Reference Document 5.1 (SRD 5.1), the public rules document for D&D fifth edition, defines an ability check as rolling a d20, adding the modifier, and succeeding if the total equals or exceeds the Difficulty Class (DC). In this tool, enter "1d20 + modifier" as the expression, enter the DC as the target and choose "or higher" to get the same check. Each face of a D20 is worth 5%, so the chance of success is (21 − (DC − modifier)) × 5%, capped between 0% and 100%.

In SRD 5.1, the rule that a natural 20 always hits applies to attack rolls; for ability checks the success test is simply total against DC. Advantage uses the higher of two d20s and disadvantage the lower. This tool does not calculate advantage separately, but if the chance of success with one die is p, it becomes 1 − (1 − p)² with advantage and p² with disadvantage. A 15 or more with no modifier (30.0%) rises to 51.0% with advantage and falls to 9.0% with disadvantage.

The Call of Cthulhu 7th Edition Quick-Start Rules work the other way: you roll 1D100 and succeed if the result is at or below your skill value. At or below half the skill is a Hard success, and at or below one fifth is an Extreme success. With a skill of 60, a regular success is 60.0%, a Hard success (30 or less) is 30.0% and an Extreme success (12 or less) is 12.0%. In this tool, use "1d100" with a target of 60 and "or lower".

How evenly do real dice land?

The biologist W. F. R. Weldon rolled 12 dice at once, 26,306 times, and counted how many showed a 5 or a 6. The statistician Karl Pearson used this data in his 1900 paper introducing the chi-squared goodness-of-fit test. The share of 5s and 6s was 0.3377, above the expected 1/3 (0.3333). Assuming fair dice, Pearson put the chance of a gap that large arising by luck at 0.000016, or "62,499 to 1".

Pearson guessed that the cause was the way the dice were made: with the pips hollowed out and opposite faces adding to seven, the face with six pips is lighter than the face with one. Labby (2009) re-rolled 12 plastic dice 26,306 times with a machine and recorded every face. The share of 5s and 6s was 0.3343, consistent with fair dice, but the six faces taken one by one were not: 1 came up 0.1686 and 6 came up 0.1688 of the time, against 1/6 (0.1667), with p = 0.00014.

If pip weight were the cause, the odds would rise steadily from 1 to 6, and Labby's data rejected that trend (p = 0.00005). Instead, a micrometer showed that the 1–6 axis was about 0.2% shorter than the other two, so the 1 and 6 faces were slightly larger. Real dice can lean from differences that small. Dice on a screen have no weight and no shape, so any difference that remains is chance.

How this tool picks each face

Each face is chosen from a 32-bit random number supplied by the browser's Web Crypto API (crypto.getRandomValues). There are 4,294,967,296 such values, which is not evenly divisible by 6 or 20, so using only the remainder would make small faces slightly more likely. To avoid that, numbers in the leftover tail beyond the largest multiple of the face count are discarded and redrawn, so every face has exactly the same chance. In a browser without Web Crypto, the tool falls back to Math.random.

Each roll is independent of the ones before it. Even after three 6s in a row on a D6, the chance of a 6 next time is still 1/6. The total probabilities come from convolving the uniform distribution of each die in turn and counting every combination, and when there are 1,000,000 combinations or fewer the tool also shows the count, as in "4 of 36 outcomes".

Common misconceptions

• "I've rolled a lot of 6s, so they're due to cool off": dice do not remember earlier results. This belief is called the gambler's fallacy, and the odds on the next roll stay the same.
• "The average is 7, so 7 or more is 50%": on 2D6, 7 or more is 58.3%. You have to consider both whether the boundary value is included and how common it is.
• "2D6 and a D12 are the same": both reach 12, but 2D6 has no 1 and clusters around 7, while the D12 spreads evenly from 1 to 12.
• "A modifier makes you luckier": a modifier moves the total by a fixed amount and leaves the shape and spread alone. Your odds rise only because you are closer to the target.
• "At or above and above are the same": in SRD 5.1 an ability check that equals the DC still succeeds. If a rule says "greater than", enter a target one higher.
• "Roll enough and the average matches exactly": the average total moves toward the expected value as you roll more, but even at 10,000 rolls it still differs in the decimals.

Limits and cautions

• Your rolls and stats live only on this screen and are neither saved nor sent to a server. They disappear on reload, so use Copy log to keep them. Copy link holds only the dice expression and target.
• Changing the kinds or number of dice or the modifier changes the distribution, so session stats and your results on the bars start over. Recent rolls are kept.
• Probabilities are calculated exactly but shown rounded to one decimal place. Anything under 0.1% is shown as "under 0.1%".
• The limit is 30 dice in total and a modifier of ±99. Rules such as advantage and disadvantage, dropping the lowest die or rerolling some dice are not calculated for you.
• This tool is for play, checks and learning. It does not legally guarantee fairness for wagers or prize draws.

As of The probabilities in this article are convolutions of fair dice (each face 1/sides, rolls independent). The cited study and rule documents (Labby 2009, SRD 5.1 and the Call of Cthulhu 7th Edition Quick-Start Rules) were checked against the original sources on 2026-10-23.

Sources

• 01Labby, Z. (2009). Weldon's Dice, Automated. CHANCE 22(4), 6–13Weldon's 26,306 throws (share of 5s and 6s 0.3377), Pearson's 1900 p = 0.000016 and pip-weight guess, the machine re-run (0.3343, face-by-face bias p = 0.00014, pip-weight trend rejected, 1–6 axis about 0.2% shorter)
• 02Wizards of the Coast. System Reference Document 5.1 (CC BY 4.0)An ability check succeeds if the total equals or exceeds the DC; advantage and disadvantage take the higher or lower of two d20s; the 20 on attack rolls
• 03Chaosium. Call of Cthulhu 7th Edition Quick-Start RulesA 1D100 at or below the skill is a regular success, at or below half a Hard success, at or below one fifth an Extreme success
• 04MDN: Crypto.getRandomValues()Cryptographically strong random numbers from the browser
• 05W3C: Web Cryptography APIThe browser standard that defines getRandomValues
• 06Lemire, D. (2019). Fast Random Integer Generation in an Interval. ACM TOMACS 29(1)How to turn random bits into an integer in a fixed range without bias

Frequently asked questions

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