Random Dice Roller
Choose a die type, set the number of dice and an optional modifier, then hit Roll. Every result updates instantly in your browser with no server needed. You get each individual die face, the grand total (with modifier), the minimum and maximum possible outcomes, and the theoretical expected value so you always know what the math says your roll should average out to.
How this dice roller works
Select a die type from the dropdown, choose how many dice to roll (1 to 20), and set an optional modifier. The Roll seed field drives the random result: every unique seed produces a unique set of rolls via a deterministic pseudo-random algorithm, so you can share or reproduce any result by sharing the seed. Change the seed by any amount to simulate re-rolling. The calculator instantly shows each individual face, the total with modifier, the minimum and maximum possible outcomes, and the theoretical expected value.
Dice notation and modifiers
Tabletop roleplaying games use the shorthand NdX+M to describe dice rolls: N is the number of dice, X is the number of sides, and M is the modifier. For example, 2d6+3 means roll two six-sided dice and add 3 to the sum. The lowest result is 2 (1+1+3=5 after the modifier) and the highest is 15 (6+6+3). The expected value is 2 x 3.5 + 3 = 10. Modifiers can be negative (representing penalties), and this calculator handles both. Understanding modifiers helps you evaluate the impact of character bonuses, weapon enchantments, or situational advantages in any dice-based game.
Probability and expected value
The expected value of a single die with S sides is (1 + S) / 2, because each face from 1 to S is equally likely. For N identical dice the expected value scales linearly to N x (1 + S) / 2. When you add a flat modifier M, the expected value becomes N x (1 + S) / 2 + M. The probability chart shown below the result plots the exact distribution of every possible total for up to five dice (for larger combinations a normal approximation applies). The distribution of multiple dice rolls follows a bell-curve shape that becomes more pronounced as you add more dice: rolling 4d6 and dropping the lowest is more likely to land near 12 than near 4 or 24.
Custom dice and rare polyhedral types
Standard polyhedral sets include the D4, D6, D8, D10, D12, and D20. The D100 (also called a percentile die) is used for percentage checks, loot tables, and wild magic surges. Beyond these, unusual sided dice (D3, D7, D14, D30) exist as physical objects and are simulated here with the custom sides option. Any integer from 2 to 1000 is supported. Non-standard dice are useful for custom game mechanics, probability education, and generating weighted random results in a wider range.
Standard polyhedral dice - quick reference
| Die | Sides | Range (1 die) | Average (1 die) | Common use |
|---|---|---|---|---|
| D4 | 4 | 1-4 | 2.5 | Daggers, small damage in D&D |
| D6 | 6 | 1-6 | 3.5 | Most board games, attribute rolls |
| D8 | 8 | 1-8 | 4.5 | Longswords, healing dice |
| D10 | 10 | 1-10 | 5.5 | Percentile (2xD10), firearms |
| D12 | 12 | 1-12 | 6.5 | Greataxe, barbarian hit die |
| D20 | 20 | 1-20 | 10.5 | Core attack and ability check die in D&D |
| D100 | 100 | 1-100 | 50.5 | Percentile checks, loot tables |
Common dice used in tabletop RPGs, board games, and probability education.
Frequently asked questions
How do I re-roll?
Change the Roll seed field by any amount and the calculator immediately produces a fresh set of rolls. You can tap the up arrow once to increment it by 1 for a quick re-roll, or type any new number. The seed is just a starting number for the random algorithm - each different value gives a completely different result.
What does the modifier do?
The modifier is a flat number added to (or subtracted from) the total of your dice. In D&D 5e, your ability score modifier, proficiency bonus, or spell attack bonus is added this way. A +3 modifier on 2d6 raises both the minimum (from 2 to 5) and maximum (from 12 to 15) by exactly 3, and lifts the average from 7.0 to 10.0.
What is the expected value and why does it matter?
Expected value is the long-run average across an infinite number of rolls. For a D20 it is 10.5: if you rolled a D20 thousands of times and averaged all the results, you would converge on 10.5. It matters because it lets you compare options - rolling 2d6 (expected 7.0) and rolling 1d12 (expected 6.5) have the same range endpoints (2 vs 1, 12 vs 12) but the 2d6 has a higher average and a bell-curve distribution, meaning extreme results are much less common.
What is D&D advantage and how do I simulate it?
Advantage means rolling 2d20 and keeping the higher result. Disadvantage means rolling 2d20 and keeping the lower. To simulate this here, roll a D20 with seed 1 and note the total, then roll again with seed 2. Compare the two to apply advantage or disadvantage. The average result with advantage on a D20 is about 13.8, versus 10.5 for a straight roll.
How does the probability calculation work?
For up to five dice with up to 20 sides each, this calculator uses an exact dynamic programming approach: it counts every possible combination of faces that produces each total, then divides by the total number of outcomes. For larger combinations it switches to a normal approximation, which is accurate within a fraction of a percent for most practical purposes.
Can I roll more than 20 dice?
The current maximum is 20 dice per roll, which covers virtually every standard tabletop scenario. Rolling 20d6 gives a total between 20 and 120 with an expected value of 70. If you need to simulate larger pools, note that by the central limit theorem the distribution approaches a normal curve, so you can use the expected value and standard deviation (square root of N times (S squared - 1) / 12) to estimate probabilities analytically.