Everyday
Dice Roller
Use this dice roller when you need physical-dice results without physical dice: board games, D&D and other tabletop RPGs, probability homework, or picking a random number.
Choose how many dice, pick the die type (d4 through d100), and add a modifier like +3 for an attack bonus. Along with the rolled total, it shows the math a die roll implies: the theoretical minimum, maximum, and expected value, so you can tell whether a roll was lucky, unlucky, or dead average. Every roll comes from a seed number, so a roll can be repeated exactly or rerolled by changing the seed.
How many dice to roll at once, from 1 to 100.
The d-number is the number of faces: a d20 rolls 1 through 20.
DnD-style bonus or penalty, like +5 or -2. Added once to the total, not to each die.
Any whole number. The same seed with the same dice always gives the same rolls, so a result can be shared or checked. To roll again, change the seed: 2, 3, 47, your lucky number.
Try an example
Result
Total (rolls + modifier)
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- Individual rolls
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- Sum of dice
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- Average per die
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- Lowest possible total
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- Highest possible total
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- Expected (average) total
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More details (1 more)
- Seed used
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the dice roller solves
Use this dice roller when you need physical-dice results without physical dice: board games, D&D and other tabletop RPGs, probability homework, or picking a random number. Choose how many dice, pick the die type (d4 through d100), and add a modifier like +3 for an attack bonus. Along with the rolled total, it shows the math a die roll implies: the theoretical minimum, maximum, and expected value, so you can tell whether a roll was lucky, unlucky, or dead average. Every roll comes from a seed number, so a roll can be repeated exactly or rerolled by changing the seed.
Formula
How to use it
- Choose how many dice to roll, from 1 to 100.
- Pick the die type: d4, d6, d8, d10, d12, d20, or d100.
- Enter a modifier such as +5 or -2 if your game adds a bonus or penalty to the total; leave it at 0 otherwise.
- Read the total, then check the expected value to see whether the roll came in high or low.
- To roll again, change the roll seed to any other whole number. Keep the seed to repeat or share an exact roll.
How to read the answer
The primary total is the rolled sum plus your modifier, which is the number you use in-game. Compare it to the expected value: a 2d6 roll averages 7, so an 11 is a strong roll and a 3 is a weak one. The minimum and maximum show the full possible range, and the average-per-die line tells you how the individual dice ran relative to their (sides + 1) / 2 average. The seed is the only source of randomness: the same seed, dice, and modifier always reproduce the same rolls.
Common mistakes and edge cases
- The modifier is added once to the total, not once per die: 3d6+2 tops out at 20, not 24.
- Expected value is a long-run average, not a prediction: any single roll can land anywhere in the range.
- Rolling 2d6 is not the same as rolling 1d12: two dice cluster near the middle (7 is the most common 2d6 sum), while one die is equally likely to land on any face.
- The percent of values in a data set that fall at or below a given value. conventions vary: this d100 rolls 1 through 100, but some tabletop systems read paired d10s as 00-99.
- A negative modifier can push the total to zero or below; this roller reports the true total rather than clamping it to 1, so apply any house-rule minimum yourself.
- Recalculating with the same seed repeats the same roll. That is deliberate, so results can be checked and shared; change the seed for a fresh roll.
Worked examples
Classic board game roll: 2d6
Two six-sided dice with no modifier and the default seed of 1: the dice show 4 and 1 for a total of 5, two below the expected value of 2 x 3.5 = 7. Any 2d6 total lands between 2 and 12.
Total (rolls + modifier)
5
D&D attack roll: 1d20+5 (natural 1)
One twenty-sided die plus a +5 bonus. Seed 7 rolls a natural 1, so the total is 1 + 5 = 6, the lowest possible; the expected value is (20 + 1) / 2 + 5 = 15.5.
Total (rolls + modifier)
6
Negative modifier: 4d6-3
Four six-sided dice with a -3 penalty. Seed 3 rolls 5, 1, 3, 1 for a sum of 10 and a total of 7. The range is 1 (four 1s minus 3) to 21, and the expected value is 4 x 3.5 - 3 = 11.
Total (rolls + modifier)
7
Percentile roll: 1d100
A single 1-to-100 roll, useful for percent-chance checks: rolling at or under 30 happens 30% of the time. Seed 42 lands on 61, just above the expected value of (100 + 1) / 2 = 50.5.
Total (rolls + modifier)
61
Same seed, same roll
Re-running 2d6 with seed 1 reproduces the first example exactly: 4 and 1 again, total 5. Randomness lives entirely in the seed, which is what makes rolls shareable.
Total (rolls + modifier)
5
Too many dice
The roller caps at 100 dice, so 250d6 is rejected with a clear message.
Total (rolls + modifier)
Error
Frequently asked questions
Is this dice roller fair?+
Each die is drawn from a seeded pseudo-random generator (mulberry32) with every face equally likely, so over many rolls it behaves like a well-balanced physical die for games, classrooms, and homework. It is pseudo-random rather than truly random, which means it is not suitable for cryptography or real-money gambling.
What does d20 (or 2d6+3) mean?+
Dice notation is NdS+M: N is how many dice, S is the number of sides, and M is a modifier added to the total. So d20 is one twenty-sided die, and 2d6+3 means roll two six-sided dice, add them, then add 3.
How is the expected value computed?+
A fair die with S sides averages (S + 1) / 2 per roll, because the faces 1 through S average to that midpoint: a d6 averages 3.5. Multiply by the number of dice and add the modifier: 2d6+3 has an expected value of 2 x 3.5 + 3 = 10.
How do I roll again?+
Change the roll seed to any other whole number and recalculate. The seed is the only source of randomness, so seed 1 always gives one specific roll, seed 2 another, and so on. Keeping the seed the same repeats the roll exactly, which is handy for sharing a result or checking a friend's claim of a natural 20.
Why does the same seed always give the same roll?+
A seeded generator starts from the seed and follows a fixed recipe, so the sequence of faces is determined the moment you pick the seed. That is how the worked examples on this page can state an exact total. The theoretical rows (minimum, maximum, and expected value) never depend on the seed at all.
Can I roll different dice together, like 2d6 + 1d8?+
This roller uses one die type per roll. To mix dice, roll each group separately and add the totals; the expected values add the same way, so 2d6 + 1d8 averages 7 + 4.5 = 11.5.
Are two d6s the same as one d12?+
No. Both share part of their range, but 1d12 is uniform (every result 1-12 has probability 1/12), while 2d6 runs 2-12 and clusters near 7, which is why 7 dominates so many dice games.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Rolls come from a seeded mulberry32 pseudo-random generator, so the same seed, dice count, and die type always reproduce the same rolls; results are for games and classroom use, not security or gambling.
- Each face is equally likely; expected value uses the fair-die average of (sides + 1) / 2 per die.
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Last updated: September 4, 2026