Calculator
Dice Probability Calculator
Set any number of dice, get the exact odds of every total and the chance of hitting a target or better, then roll them. Every figure is enumerated from the full outcome space, never estimated by simulation.
The shape of 2d6
Change the inputs above and this whole section recomputes. The tall bars are where the notation actually lands.
- Lowest
- 2
- Highest
- 12
- Average
- 7.00
- Most likely
- 7
- Chance of 7
- 16.7%
- Possible totals
- 11
Peak at 7 (16.7%). Average 7.00. Range 2–12.
Every total, with odds
This or higher is the number you want for a target: the chance of meeting or beating it.
| Total | Chance | Odds | This or higher | This or lower |
|---|---|---|---|---|
| 2 | 2.78% | 1 in 36 | 100.0% | 2.78% |
| 3 | 5.56% | 1 in 18 | 97.2% | 8.33% |
| 4 | 8.33% | 1 in 12 | 91.7% | 16.7% |
| 5 | 11.1% | 1 in 9 | 83.3% | 27.8% |
| 6 | 13.9% | 1 in 7 | 72.2% | 41.7% |
| 7 | 16.7% | 1 in 6 | 58.3% | 58.3% |
| 8 | 13.9% | 1 in 7 | 41.7% | 72.2% |
| 9 | 11.1% | 1 in 9 | 27.8% | 83.3% |
| 10 | 8.33% | 1 in 12 | 16.7% | 91.7% |
| 11 | 5.56% | 1 in 18 | 8.33% | 97.2% |
| 12 | 2.78% | 1 in 36 | 2.78% | 100.0% |
How to read the numbers
The Chance column is the probability of that exact total. Odds is the same figure written as one in so many rolls. This or higher adds up every total from that row to the top, which is what you need when a rule says "roll 15 or better". This or lower is the reverse, for roll-under systems.
For a single die every row is identical, because every face is equally likely. Add a second die and the middle rows swell while the ends thin out, and by the third die the curve is unmistakable. That is the whole reason 3d6 and 1d20 feel so different at the table even though their averages are almost the same.
More dice, or bigger dice
Every dice system is built from two levers. Adding dice makes a roll steadier. Making the dice bigger makes it flatter. The inputs above are the quickest way to feel the difference, and the figures below are what they show.
Take ten d6. The range runs 10 to 60, but the standard deviation is only 5.4, and 95.0% of rolls land between 25 and 45. The maximum is 1 in 60,466,176. Most people expect more dice to mean a wilder result; it means the opposite. A pool that size cannot really surprise you, it can only come in a little above or below 35, which is why a designer who wants an effect to reliably finish off a tier of creature reaches for many small dice rather than one big one.
Now hold the count at three and change the faces. 3d6 peaks at 10 and 11 with 12.5% each. 3d10 covers nearly twice the ground with the same rounded hump, but its peak at 16 and 17 is only 7.5%, because ten faces per die means many more ways to reach any total and the probability spreads thinner. More faces flatten the curve for the same number of dice; more dice steepen it for the same faces.
Around six dice the sum is close enough to a bell curve that the usual rules of thumb start to work. 6d6 averages 21 with a standard deviation of 4.2, and the window one deviation either side, 17 to 25, catches 71.1% of rolls, close to the textbook two thirds. That is the central limit theorem, drawn in dice.
Same dice, different rule
How dice are combined matters more than how many there are. Two d10s read as tens and units give a flat 1 to 100, every result exactly 1%: that is a percentile roll. The same two dice added give 2 to 20, with 11 at 10.0% and each end at 1.00%. If a rule says percentile and you add instead, you will almost never see the tails, and any table built on flat weights quietly stops working.
Two d20s are the same trap. Advantage keeps the higher one, so the result is still 1 to 20: a natural 20 becomes 9.75% and the average rises to 13.8. Added together, 2d20 runs 2 to 40, averages 21, and puts 5.00% on 21 and 0.250% on each end. A rule that says succeed on 15 or better is a 30.0% chance on one die, 51.0% with advantage, and 77.2% if someone adds the two dice by mistake. The d20 page has the advantage toggle and the full table of what it is worth.
Common questions
How is dice probability calculated?
Dice probability is calculated by counting outcomes. For one die each face has a 1 in N chance. For several dice, this calculator convolves the distributions: it enumerates every combination of faces, adds them up, and counts how many combinations produce each total. Divide by the total number of combinations and you have the exact probability, with no sampling error.
What are the odds of rolling a 7 on 2d6?
The odds of rolling a 7 on 2d6 are 16.7%, or 1 in 6. Six of the thirty-six combinations add to 7, more than any other total, which is why 7 is the most common roll of two dice.
What is the probability of rolling at least a 10 on 2d6?
The probability of rolling 10 or higher on 2d6 is 16.7%, or 1 in 6. Only six combinations reach 10, 11 or 12: two ways to make 11, three to make 10, and one to make 12.
Does this calculator handle modifiers and drop lowest?
Yes. A modifier shifts every total by that amount without changing the shape of the curve. For drop-lowest rolls, use the 4d6 drop lowest stat roller, which computes that distribution exactly and also ranks a full six-score array.
Common rolls
Each one loads into the calculator and roller above.