1. Enter the number of dice and the sides per die. Two six-sided dice are written 2d6, so N = 2 and S = 6.
2. Pick what you want to happen: a total (exactly, at least or at most X), a face on at least one die, a face on every die, or k dice that reach X.
3. Type the target X, and k for the two "k dice" modes. The result updates as you type.

Dice probability is the share of equally likely outcomes that meet a condition. A fair die gives each face the same chance, so a d6 shows each number with probability 1/6. OpenStax calls the full list of outcomes the sample space and any group of outcomes an event.

Board gamers, tabletop role players, teachers and game designers use it for the same task: deciding whether a roll is worth the risk. A dice probability figure is a long-run rate. It never predicts the next roll, and a die has no memory of past results. For the odds language behind "1 in 6", see probability vs odds.

The calculator counts favorable outcomes exactly and divides by the total number of outcomes, S to the power N. It never estimates or simulates.

1. Sums: the tool builds the count of every total one die at a time. Each new die spreads each earlier total over S new totals. This gives the same numbers as the closed formula on Wolfram MathWorld, without rounding.
2. At least one: it uses the complement. At least one 6 on N dice = 1 - (5/6)^N, because "no 6 at all" is the only way to fail.
3. All dice: each die must pass on its own, so the chances multiply. Every die 3 or higher on 4d6 = (4/6)^4 = 16/81.
4. k of N dice: it uses the binomial formula C(N,k) x p^k x (1 - p)^(N - k), where p is the chance that one die reaches X. See the combination calculator for C(N,k) on its own.

All counts use whole-number arithmetic, so 50d100 still gives an exact fraction.

Say you roll three six-sided dice and need a total of exactly 10.

1. Total outcomes: 6^3 = 216.
2. Ways to make 10: 27 (for example 1-3-6, 2-4-4 and 3-3-4 in every order).
3. Probability: 27 / 216 = 1 / 8 = 12.50%.

A total of 11 also has 27 ways, so 10 and 11 tie as the most likely totals on 3d6. The average total is 10.5 with an SD of 2.958. A 3 or an 18 each has only 1 way in 216, which is 0.46%.

Number of Dice

More dice pull the total toward the middle. One d6 is flat: every total has 1/6. Two d6 form a triangle that peaks at 7. Ten d6 look close to a bell curve, and a total of 35 or more has 53.63%.

Sides per Die

More sides spread the chances thinner. One exact face is 1/6 on a d6 but 1/20 on a d20, which is 5%.

Exact Versus Threshold Targets

"Exactly 8" on 2d6 is 5/36 = 13.89%, but "8 or more" is 15/36 = 41.67%. Choose the mode that matches the rule you are playing.

At Least One Grows Fast

At least one 6 is 16.67% with one die, 42.13% with three dice and 51.77% with four dice. It never reaches 100%, since all dice can miss.

Dice pool systems that count successes, such as many wargames, use the k-of-N modes. For a full attack chain with hit, wound and save rolls, use the 40K dice calculator.

Game Night Decisions

Check whether a risky roll is worth it before you commit. Needing a 15 or higher on a d20 is 30%, so a safer play often wins.

Teaching Probability

Dice make sample spaces concrete. Students can compare the exact 1/6 with their own tally and see the gap shrink as rolls add up.

Game Design and Balance

Designers test whether a mechanic is too swingy. Replacing 1d12 with 2d6 keeps the range close but makes the middle much more common.

1. Adding Chances for at Least One

Three dice do not give 3 x 1/6 = 50% for at least one 6. The correct value is 1 - (5/6)^3 = 42.13%, because the chances overlap.

2. Treating Totals as Equally Likely

On 2d6, a 7 has 6 ways and a 2 has 1 way. Only single faces on one die are equally likely.

3. the Gambler's Fallacy

A 6 is never "due" after a dry spell. Each roll is independent, as OpenStax explains for independent events. The same idea applies to loot drop odds.

4. Mixing Up Exactly and at Least

"Exactly 2 sixes" and "at least 2 sixes" are different events. The second is always equal or larger.

5. Reading a Rare Event as Impossible

A 1-in-100 result appears about once in every 100 tries over time. Long shots still happen at the table.

Every probability here is exact for fair dice, because the tool counts outcomes with whole numbers instead of sampling.

7 is the most likely total on two six-sided dice, with 6 ways out of 36, or 16.67%. The totals 2 and 12 are the least likely at 1/36 each, which is 2.78%.

The chance is 1 in 6, or 16.67%, on a fair six-sided die. On a d20 a single face is 1 in 20, or 5%.

The chance is 671/1296, or 51.77%. Four dice is the smallest number that makes at least one 6 more likely than not.

Doubles come up 6 times in 36 outcomes, which is 1/6 or 16.67%. Set 2 dice, 6 sides and "All dice equal X" to check one specific double, such as double 6 at 1/36.

Five of a kind comes up 6 times in 7,776 outcomes, which is 1/1296 or 0.077%. The calculator gives 1/7776 for one specific face, such as five 6s.

A 7 can be made 6 ways (1-6, 2-5, 3-4, 4-3, 5-2, 6-1), but a 2 only one way (1-1). More combinations mean a higher chance.

Subtract the bonus from the target first. To reach 18 with +5, you need 13 or more on the die, which is 8/20 = 40%.

No. A d20 gives every total from 1 to 20 an equal 5%. 2d10 runs from 2 to 20 and peaks at 11, with 10%.

It handles up to 50 dice with up to 100 sides each. That keeps the exact count fast in a browser.

No. It assumes one roll of identical fair dice with no rerolls. Rerolls change the chance for each die, so they need a different model.

No. The counting runs in your browser and nothing is sent to a server. Saved results stay in your own browser storage.

• OpenStax Introductory Statistics 2e, section 3.1 Terminology (Rice University, OpenStax). Sample space, events and equally likely outcomes.
• OpenStax section 3.2 Independent and Mutually Exclusive Events (OpenStax). Why separate rolls multiply and never influence each other.
• OpenStax section 4.3 Binomial Distribution (OpenStax). The k-of-N success formula, mean np and SD.
• Wolfram MathWorld: Dice (Wolfram Research). Closed formula for the chance of p points on n s-sided dice and the 2d6 distribution.