Dice Roller
Roll any combination of dice — standard or custom-sided — with the total, each individual roll and the full probability distribution.
How to use this calculator
- 1Set the number of sides and how many dice to roll.
- 2Add a modifier for tabletop-style notation like 2d6+3.
- 3The probability table shows how likely your result was, and every other possible total.
How the calculation works
Total = Σ(individual rolls) + modifier Range = [n + m, n·s + m]- n
- Number of dice
- s
- Sides per die
- m
- Modifier added to the total
The distribution of a sum of dice is computed by convolution: the ways to reach a given total is the sum, over every possible last-die outcome, of the ways to reach the remainder with the other dice.
This is why multiple dice cluster around the middle: there is only one combination that rolls the minimum (all 1s) but many combinations that sum to the average.
Worked example
Rolling 2d6
- 1.Each die has 6 faces, so there are 6² = 36 equally likely outcomes.
- 2.A total of 7 can be made 6 ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 — a 16.7% chance, the most likely total.
- 3.A total of 2 or 12 can each be made only 1 way — a 2.8% chance each, the least likely totals.
Result: Totals cluster around 7, the most probable sum
What randomness and probability distributions mean here
Rolling a die is the simplest possible example of a random process: each face has an equal, independent chance of coming up, with no memory of any previous roll. A probability distribution just describes, across every possible outcome, how likely each one is — for a single fair die, that distribution is flat, since every face is equally likely. Once more than one die is involved, the distribution of the total is no longer flat, even though each individual die still is.
Why totals cluster around the middle
Summing multiple dice changes the shape of the distribution because there are many more ways to reach a middling total than an extreme one. Rolling two six-sided dice, there is exactly one combination that produces the minimum total of 2 (both dice showing 1) and exactly one that produces the maximum of 12 (both showing 6), but six different combinations produce a 7. The individual dice stay perfectly fair; it is the counting of combinations that makes the sum bunch toward the middle, which is the same combinatorial reasoning behind a bell-curve shape appearing in all sorts of unrelated situations.
Where dice rolling is actually used
Beyond the tabletop, this same mechanic serves several purposes:
- Tabletop role-playing games — systems like Dungeons & Dragons build entire rule sets around specific dice — a d20 for a pass/fail check, 2d6 or similar for damage — using notation like "2d6+3" to mean "roll two six-sided dice, add them, then add 3".
- Board games — countless games use dice to introduce controlled randomness into an otherwise deterministic strategy game, from a simple move-counter to combat resolution.
- Impartial decision-making — rolling a die, or flipping a coin, its two-sided cousin, is a long-standing, transparent way to make an arbitrary choice that no party can be accused of rigging.
- Teaching probability — dice are a standard teaching tool for probability and statistics precisely because the underlying sample space is small and countable enough to work out by hand, while still showing real distribution shapes.
Intuitions about randomness that don’t hold up
A couple of very common misreadings of random dice are worth naming:
- The gambler’s fallacy — a die has no memory — if it hasn’t shown a 6 in twenty rolls, the odds of a 6 on the next roll are still exactly 1 in 6, not "due" to be higher.
- Assuming every total is equally likely — this is true for a single die, but false the moment a second one is added — a common mix-up for anyone new to probability, since it seems like it should generalize and doesn’t.
- Pseudo-random versus true randomness — this tool draws from the browser’s cryptographically secure random number generator, which is unpredictable enough for games and simulations, though it is worth knowing it is still an algorithm producing numbers, not a physical die.
What this assumes, and where it stops
Assumptions
- Each die is fair — every face equally likely.
Limitations
- The full distribution table is only shown when the number of possible sums is manageable to display; very large dice pools show summary statistics only.
Common questions
Why is 7 the most common result on 2d6?
Because more combinations of two dice add up to 7 than to any other total. There are six ways to make 7 (1+6 through 6+1) but only one way to make 2 or 12. Every individual die is equally likely to show any face, but the sum of two dice is not equally distributed — it clusters toward the middle.
What does "2d6+3" mean?
Standard tabletop notation: roll two six-sided dice, add them together, then add 3. It is shorthand borrowed from Dungeons & Dragons and used throughout tabletop gaming — "XdY+Z" means X dice with Y sides each, plus a flat modifier Z.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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