Dice Roller
Roll any dice online with fair crypto randomness, then see the exact chance of your total, the average and the full probability chart for that roll.
More options
2d6: 7 is the most likely total (16.67 percent).
Odds of this roll
Exact chances for the total you rolled, worked out from every possible outcome.
Roll the dice to see the chance of your total or higher.
Your calculation
The same steps the roller runs, with your settings.
- Outcomes: 6² = 36 equally likely results.
- Totals: add one die at a time, summing the ways for the 6 totals just below each new total (convolution).
- Mean of one die: (6 + 1) ÷ 2 = 3.5, so 2 × 3.5 = 7.
- Variance of one die: (6² − 1) ÷ 12 = 2.9167, so 2 × 2.9167 = 5.8333 and the standard deviation is √5.8333 = 2.42.
Roll the dice to compare your total with the average.
Probability of each total
Each bar is one total. Taller bars are more likely, and the outlined bar holds your roll.
Every total, ways and chance
Ways out of 36 equally likely outcomes.
| Total | Ways | Chance | Or higher |
|---|---|---|---|
| 2 | 1 | 2.78% | 100% |
| 3 | 2 | 5.56% | 97.22% |
| 4 | 3 | 8.33% | 91.67% |
| 5 | 4 | 11.11% | 83.33% |
| 6 | 5 | 13.89% | 72.22% |
| 7 | 6 | 16.67% | 58.33% |
| 8 | 5 | 13.89% | 41.67% |
| 9 | 4 | 11.11% | 27.78% |
| 10 | 3 | 8.33% | 16.67% |
| 11 | 2 | 5.56% | 8.33% |
| 12 | 1 | 2.78% | 2.78% |
Roll history
Your last 10 rolls in this tab, newest first. Nothing is saved after you close the page.
- Your rolls appear here.
Rolls use crypto.getRandomValues on this device and are never sent anywhere. Probabilities are exact for fair dice; physical dice can be slightly unbalanced.
How the Dice Roller Works
This dice roller rolls any number of dice from 1 to 100, each with 2 to 1,000 sides, and adds a modifier if you enter one. It covers the full polyhedral dice set used in tabletop games (d4, d6, d8, d10, d12, d20 and the d100 percentile die) plus any custom die, so one page replaces a bag of physical dice.
Every roll has a random part, the faces and total drawn fresh each time, and a fixed part: the exact probability of every total for your settings, found by counting outcomes rather than by simulation. That is why the chart stays the same no matter what you roll.
How to Use the Dice Roller
- Number of dice: 1 to 100.
- Die type: pick a standard die, or type any side count from 2 to 1,000.
- Modifier: a whole number added to or taken from the total, such as +5 for a skill bonus.
- More options: dice notation, drop lowest or keep highest, advantage and disadvantage, a target total and exploding dice.
- Roll: press Roll, press Enter in any field, or use Roll again in the result card.
Changing a setting rolls again and updates the odds. Copy result copies a line such as 2d6 = 9 (4, 5).
Dice Notation Explained
Dice notation writes a roll as NdS+M: N dice with S sides each, plus a modifier M. The roller reads these forms:
- d20: one twenty sided die.
- 3d6+2: three d6 plus 2, totals 5 to 20.
- 4d6dl1 or 2d20kh1: drop the lowest, or keep the highest.
- 1d20+5 adv: roll twice, keep the higher total.
- 3d6! exploding dice; d% a percentile die.
Dice Probability Formulas
A fair die with s sides gives each face a chance of 1/s, and separate dice do not affect each other. The calculator uses these same formulas, so you can check any result by hand.
Expected value of dice
Variance and standard deviation
The modifier moves every total by the same amount, so it changes the mean but not the spread. Adding dice makes totals cluster: the standard deviation grows with the square root of N while the range grows with N, which is why 8d6 rarely lands far from 28.
Probability of a total (counting ways)
For more dice the roller adds one die at a time: the ways to reach a total with k dice equal the sum of the ways for the six totals just below it with k − 1 dice. This step, called convolution, gives exact counts even for 10d6 and its 60,466,176 outcomes.
Probability of at least one
Exploding dice
A die that shows its highest face rolls again and adds the new roll, so one exploding die averages (S + 1) ÷ 2 × S ÷ (S − 1). For a d6 that is 3.5 × 6 ÷ 5 = 4.2. The roller allows up to 10 extra rolls per die so the odds can be counted exactly; for a d6 the cap changes the average by less than one ten millionth. Drop and keep rules are counted face by face, which covers every outcome exactly.
2d6 Probability Chart
Two six sided dice give 6 × 6 = 36 equally likely ordered pairs. Totals near the middle can be made in more ways, so the chart rises to a peak at 7 and falls away evenly on both sides. The default roll above shows every total with its ways and chance: 2 and 12 have 1 way each (2.78 percent), 4 and 10 have 3 (8.33 percent), 6 and 8 have 5 (13.89 percent).
The probability of rolling a 7 with two dice is 6 ÷ 36 = 1/6, or 16.67 percent, and a 7 comes up on average once every 6 rolls. A 6 or an 8 covers 10 of 36 outcomes (27.78 percent), a 7 or 11 covers 8 of 36 (22.22 percent), and 2, 3 or 12 covers 4 of 36 (11.11 percent).
Chance of Rolling at Least One Six
Asking for at least one six is easier to answer through its opposite: the chance that no roll shows a six is (5/6)ⁿ, and the answer is 1 minus that. Rolling n dice at once gives the same result as rolling one die n times.
| Rolls or dice | P(no six) | P(at least one six) |
|---|---|---|
| 1 | 83.33% | 16.67% |
| 2 | 69.44% | 30.56% |
| 4 | 48.23% | 51.77% |
| 6 | 33.49% | 66.51% |
| 10 | 16.15% | 83.85% |
| 12 | 11.22% | 88.78% |
Four rolls is the first point where a six is more likely than not. For double sixes with two dice (1/36 per throw), 24 throws reach only 1 − (35/36)²⁴ = 49.14 percent, and 25 throws (50.55 percent) pass even odds. Six rolls do not guarantee a six: 33.49 percent of the time none appears.
Polyhedral Dice Set: Averages and Spread
A standard set of polyhedral dice holds a d4, d6, d8, d10, d12 and d20, often with a second d10 marked in tens for a d100. The roller numbers every die from 1 to its side count.
| Die | Average | Variance | Std deviation |
|---|---|---|---|
| d4 | 2.5 | 1.25 | 1.118 |
| d6 | 3.5 | 2.9167 | 1.708 |
| d8 | 4.5 | 5.25 | 2.291 |
| d10 | 5.5 | 8.25 | 2.872 |
| d12 | 6.5 | 11.9167 | 3.452 |
| d20 | 10.5 | 33.25 | 5.766 |
| d100 | 50.5 | 833.25 | 28.866 |
A single die is flat: each face of a d20 has a 5 percent chance and each face of a d100 has 1 percent. A peak appears only when you add dice together.
4d6 Drop Lowest: Ability Score Odds
The Dungeons & Dragons Basic Rules generate each ability score by rolling four six sided dice and adding the highest three, six times over. Counting all 6⁴ = 1,296 outcomes gives the exact chance of every score from 3 to 18.
| Score | Ways | Chance | Score | Ways | Chance |
|---|---|---|---|---|---|
| 3 | 1 | 0.08% | 11 | 148 | 11.42% |
| 4 | 4 | 0.31% | 12 | 167 | 12.89% |
| 5 | 10 | 0.77% | 13 | 172 | 13.27% |
| 6 | 21 | 1.62% | 14 | 160 | 12.35% |
| 7 | 38 | 2.93% | 15 | 131 | 10.11% |
| 8 | 62 | 4.78% | 16 | 94 | 7.25% |
| 9 | 91 | 7.02% | 17 | 54 | 4.17% |
| 10 | 122 | 9.41% | 18 | 21 | 1.62% |
The average score is 12.24 (12.2446 to four places) with a standard deviation of 2.85, and 13 is the most likely result. A score of 15 or higher comes up 23.15 percent of the time, and 8 or lower 10.49 percent. Six rolled scores average 73.47 in total, a little above the 72 points of the standard set 15, 14, 13, 12, 10 and 8 that the rules offer instead of rolling.
Advantage and Disadvantage Odds on a d20
Under the D&D rules, advantage means rolling a second d20 and using the higher roll, and disadvantage means using the lower. For a target X on a single d20, the chance of reaching it is (21 − X) ÷ 20. Both dice must miss for advantage to miss, which gives the formulas in the table header.
| Target | Normal | Advantage: 1 − ((X − 1)/20)² | Disadvantage: ((21 − X)/20)² |
|---|---|---|---|
| 5 | 80% | 96% | 64% |
| 8 | 65% | 87.75% | 42.25% |
| 10 | 55% | 79.75% | 30.25% |
| 11 | 50% | 75% | 25% |
| 13 | 40% | 64% | 16% |
| 15 | 30% | 51% | 9% |
| 18 | 15% | 27.75% | 2.25% |
| 20 | 5% | 9.75% | 0.25% |
The average d20 roll is 10.5. With advantage it rises to 13.825 and with disadvantage it falls to 7.175, a shift of about 3.3 points either way. The gain is largest for middle targets: at 11, advantage adds 25 percentage points, while at 20 it adds under 5. In the roller, Advantage rolls your whole setting twice and keeps the higher total, so it also works for 1d20+5.
Is an Online Dice Roller Fair?
A roller is fair when every face has the same chance and no roll can be predicted from the ones before it. This page draws its random numbers from crypto.getRandomValues, which MDN documents as a cryptographically strong generator seeded with enough entropy. NIST publishes the SP 800-90 series of standards for this kind of deterministic random bit generator.
Turning a random number into a die face needs care. A random byte has 256 values, and 256 ÷ 6 leaves a remainder of 4, so taking a byte modulo 6 would give faces 1 to 4 a chance of 43/256 = 16.8 percent and faces 5 and 6 only 42/256 = 16.41 percent. This roller draws 32 bit values instead and uses rejection sampling: since 2³² divided by 6 leaves 4, the top 4 of 4,294,967,296 values are thrown away and drawn again. Every face is then exactly equally likely.
You can test fairness yourself. In 60,000 rolls of a d6 each face should appear about 10,000 times with a standard deviation of about 91, so counts between roughly 9,817 and 10,183 are normal about 95 percent of the time. Three sixes in a row has a chance of 1 in 216.
Where People Use a Dice Roller
- Board games: replace lost dice or roll for a whole table.
- Tabletop RPGs: d20 checks, damage such as 8d6 (average 28) and 4d6 drop lowest ability scores.
- Classroom lessons: roll 2d6 a hundred times and compare the tally with the exact chart.
- Quick decisions: a d100 for a percent chance, or a custom die to pick among options.
For a plain range such as 50 to 500, use the Random Number Generator. For general events try the Probability Calculator, and for counting arrangements the Permutation and Combination Calculator.
Common Mistakes
- Treating totals as equally likely. On 2d6 a 7 is six times as likely as a 2.
- Adding chances for repeated rolls. Four rolls give 51.77 percent for a six, not 4 × 16.67 = 66.67 percent.
- Expecting a due number. Dice have no memory; a six is 1/6 after any streak.
- Using the formula mean for drop rules. 4d6 drop lowest averages 12.24, not 3 × 3.5 = 10.5.
Frequently Asked Questions
What is the probability of rolling a 7 with two dice?
Two six sided dice have 6 × 6 = 36 equally likely ordered outcomes, and six of them add up to 7: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, and 6 and 1. The probability is 6 ÷ 36 = 1/6, or 16.67 percent, which makes 7 the most likely total. The totals 6 and 8 come next with 5 ways each (13.89 percent), while 2 and 12 have only one way each, a chance of 1 in 36 or 2.78 percent.
Is an online dice roller truly random?
This dice roller uses crypto.getRandomValues, the browser function that MDN describes as producing cryptographically strong random values from a generator seeded with enough entropy. Each 32 bit value becomes a face through rejection sampling: the few values above the largest multiple of the number of sides are thrown away and drawn again, so every face has exactly the same chance. Rolls happen on your device, are not sent to a server, and cannot be predicted from earlier rolls. Over 60,000 rolls of a d6, each face should land close to 10,000 times.
What is the average of 4d6 drop lowest?
Rolling four six sided dice and adding the highest three gives an average of 12.24 per ability score. Counting all 6⁴ = 1,296 outcomes shows that the most likely score is 13 at 13.27 percent, an 18 has 21 ways (1.62 percent) and a 3 has just 1 way (0.08 percent). Six scores average about 73.47 in total, slightly above the 72 points of the standard set 15, 14, 13, 12, 10 and 8 offered in the D&D Basic Rules. The standard deviation of one score is 2.85.
How much does advantage help on a d20 roll?
With advantage you roll two d20s and keep the higher, so the chance of reaching a target X becomes 1 − ((X − 1) ÷ 20)². Against a target of 11 the chance rises from 50 percent to 75 percent, and against 15 it rises from 30 percent to 51 percent. The average roll climbs from 10.5 to 13.825, about 3.3 points. Disadvantage mirrors this: the chance becomes ((21 − X) ÷ 20)², so a target of 15 drops to 9 percent and the average falls to 7.175.
What is the chance of rolling at least one six?
The chance of no six on one roll is 5/6, so the chance of at least one six in n rolls is 1 − (5/6)ⁿ. Two rolls give 30.56 percent, four rolls give 51.77 percent, six rolls give 66.51 percent and ten rolls give 83.85 percent. Four rolls is the smallest number that makes a six more likely than not. Rolling n dice at once gives the same answer as rolling one die n times, because each die is independent of the others.
What does dice notation like 3d6+2 mean?
Dice notation writes a roll as NdS+M: N is the number of dice, S is the number of sides on each die and M is a fixed modifier added to the total. So 3d6+2 means roll three six sided dice, add them and add 2, giving totals from 5 to 20 with an average of 12.5. A missing N means one die, so d20 is a single twenty sided die, and d% is a percentile die from 1 to 100. Extra codes such as dl1 (drop lowest one) or kh3 (keep highest three) change which dice count.
Sources & References
- MDN Web Docs. Crypto: getRandomValues() method. developer.mozilla.org
- National Institute of Standards and Technology. SP 800-90A Rev. 1, Recommendation for Random Number Generation Using Deterministic Random Bit Generators, June 2015. csrc.nist.gov
- Wizards of the Coast. D&D Basic Rules (2014), Using Ability Scores: Advantage and Disadvantage. dndbeyond.com
- Wizards of the Coast. D&D Basic Rules (2014), Step by Step Characters: ability scores. dndbeyond.com
- Portland Community College. Math in Society: Theoretical Probability (sums of two dice). spot.pcc.edu
- University of California, Berkeley. Discrete Probability Worksheet 4 Solutions (mean 7/2 and variance 35/12 of a d6). math.berkeley.edu
Probabilities assume fair, independent dice and were recomputed with the same code the roller runs. Results are for games, teaching and entertainment. Methodology reviewed: 2026.