Dice Roller
Roll 1 to 10 dice with 4 to 100 sides, add a modifier for notation like 2d6+3, and get the throw together with the exact chance of every possible total — not a simulation, the real distribution.
Enter your details above — results update as you type.
Formula and calculation
Worked example
Two six-sided dice, no modifier: the average total is 7, the standard deviation is 2.4152, and 7 is the most likely total, coming up 16.67% of the time. In the notation players use, this pool is 2d6.
Reading and using dice notation
Tabletop games write a dice pool as number-d-sides, with a modifier after it: 2d6+3 means roll two six-sided dice and add 3. A little algebra makes the notation readable. A modifier shifts every total and the average by the same amount and leaves the spread untouched, while adding a die changes both the average and the spread.
The shape of the distribution is why 2d6 feels steady and 1d20 feels like a coin flip with extra steps. Two dice already cluster near the middle, and by four dice the outline is basically a bell curve. The table under the result gives every total and its exact chance, so you can price a risky roll before you commit to it.
What the results mean
- Total
- The sum of the dice plus your modifier — one throw, from the browser's cryptographic random source. Press Roll again for a fresh one.
- Roll
- The individual dice that came up, written out, so you can check the sum and report the roll to the rest of the table.
- Average total
- The average total over many rolls: dice × (sides + 1) ÷ 2, plus your modifier. It is the balance point of the distribution, and over a long session your average total converges on it.
- Standard deviation
- The standard deviation — how far a typical roll lands from that average. Roughly two thirds of rolls fall within one standard deviation of the mean, which is what makes 2d6 feel steady and 1d20 feel wild.
- Most likely total
- The single most likely total for one roll. When several totals tie, the lowest is shown: on a single die every total is equally likely, so the mode is just the lowest number.
- Chance of the most likely total
- The chance of rolling that most likely total, in percent. On 2d6 it is the 6 in 36 that make 7; on 1d20 it is the flat 5% every face has.
- Dice notation
- Your dice pool in the notation players use — 2d6+3 means two six-sided dice plus three. Every total is shifted by the modifier.
Frequently asked questions
What are the odds of rolling a 7 with two dice?
Six of the 36 equally likely outcomes total 7, so the chance is 6 in 36, or 16.67% — the single most likely total on 2d6. The extremes are rarer than they feel: a 2 or a 12 each happen once in 36, about 2.78%.
How do I roll a d100 or percentile dice?
Choose 100 sides: the roller then returns a single number from 1 to 100, exactly like real percentile dice. Rolling two d10s as tens and units gives the same flat spread from 1 to 100, and the odds here match it.
Is this dice roller fair?
Each die comes from the Web Crypto API with a rejection-sampling step that removes modulo bias, so every face has an equal chance. Physical dice are the ones with a real fairness problem — casino dice are machined to tight tolerances and retired early for exactly that reason.
Does a modifier change the odds?
It shifts every total and the average by the same amount and leaves the shape alone. 2d6+3 rolls from 5 to 15 with an average of 10 instead of 7, while the standard deviation stays at 2.42. A bonus moves what you can reach without making the roll any swingier.
Why is 10 the most likely total for 3d6?
Of the 216 possible outcomes, 27 total 10 and another 27 total 11, so those two tie at 12.5% each. This calculator shows the lower of tied totals, which is why 10 is displayed; the distribution table lists every total with its exact count.