What does notation like 3d6 mean?

The number before the d is how many dice, and the number after it is how many sides each has. So 3d6 is three six-sided dice, 1d20 is a single twenty-sided die, and 2d10 is two ten-sided dice. The total is the sum of the faces rolled.

Are the probabilities exact or simulated?

Exact. They come from counting every possible combination by convolution, not from sampling. The simulator is separate, and exists to show how observed frequencies converge on those exact values as the number of rolls grows.

Why is seven the most likely total on 2d6?

Because it has the most combinations. Six of the thirty-six equally likely outcomes sum to seven, against only one for two and one for twelve. The further a total is from the middle, the fewer ways there are to reach it, which is what produces the triangular shape.

How do I find the chance of rolling at least a certain total?

Set the comparison to at least and enter the target. The headline figure is the cumulative probability, and the table also shows a running cumulative column if you want to read several thresholds at once.

Why does the shape become a bell curve with more dice?

Because summing independent random values tends towards a normal distribution, which is the central limit theorem. With one die every outcome is equally likely; with several, middling totals have vastly more combinations than extreme ones, and the curve tightens as you add dice.

Does it handle modifiers, such as 2d6 plus 3?

Not directly, but the adjustment is simple: subtract the modifier from your target and ask the same question of the unmodified dice. Needing at least 10 on 2d6 plus 3 is the same as needing at least 7 on 2d6, which the tool answers directly.

What about advantage, or rolling several and keeping the highest?

Those mechanics are not sums, so they are outside what this calculator models. Rolling twice and keeping the better result has a different distribution from rolling once, and mechanics that drop the lowest of four dice need their own treatment. This tool covers the sum of N dice with M sides.

Why does my simulated result differ from the exact probability?

Because that is how randomness behaves at small sample sizes. Twenty rolls can easily land ten percentage points away from the true value; several hundred will usually be close. Watching the gap narrow is one of the more useful things the simulator does.

Can I use this for games other than tabletop RPGs?

Yes. Any question about the sum of several uniform random values has the same structure, whether it concerns a board game, a probability exercise or a sanity check on a simulation. The dice framing is just the most familiar way to express it.

Are the dice settings sent to a server?

No. The calculation and the simulation both run in your browser, and nothing you enter leaves the page.

Dice Probability Calculator – 2d6, 3d6, 1d20 Odds

Dice Probability Calculator

// NUMBER OF DICE (N)

// SIDES (M)

// NOTATION

2d6

// CONDITION

// TARGET

Range: 2 – 12

// ROLL THE DICE

↑ Press the button and the result appears here

// PROBABILITY THAT THE TOTAL IS ≥ 7

58.33%

Mean

7.00

Std. deviation

2.42

Mode

Range

2〜12

// PROBABILITY DISTRIBUTION

// PROBABILITY OF EVERY TOTAL

Total

Ways

Probability

Cumulative

2.78%

5.56%

8.33%

16.67%

11.11%

27.78%

13.89%

41.67%

16.67%

58.33%

13.89%

72.22%

11.11%

83.33%

8.33%

91.67%

5.56%

97.22%

2.78%

> 99.99%

// SUMMARY

2d6, total ≥ 7 → probability 58.33% (mean 7.00, standard deviation 2.42)

// Dice Probability Calculator: Features

Exact probabilities, not estimates

The distribution is computed by convolution, counting the number of ways each total can be reached rather than sampling. That means the figures are exact: for two six-sided dice, a total of seven occurs in six of the thirty-six equally likely outcomes, which is exactly one in six. Every total, its number of combinations, its probability and the running cumulative total are listed, so you can read off at-least and at-most questions directly.

Why multiple dice cluster in the middle

A single die is flat: every face is equally likely. Add a second and the shape changes completely, because there are six ways to make seven and only one to make two. With three or more dice the distribution approaches a bell curve, which is the central limit theorem showing up in a very concrete form. It is also why 3d6 for a character statistic produces mostly average results while 1d20 produces genuinely swingy ones, and why systems choose one or the other deliberately.

The comparison operators

Most practical questions are not about an exact total but about clearing a threshold: whether a roll reaches a target number, or stays under a limit. Setting the comparison to at least, at most, greater than or less than gives the cumulative probability directly, rather than requiring you to add up rows of the distribution yourself. The headline figure updates as you change the target, which makes it easy to see how much difference a single point of modifier makes.

The simulator, and what it teaches

Rolling the dice for real alongside the exact figure shows how slowly randomness converges. Twenty rolls of 2d6 frequently produce an observed frequency far from the true value; a few hundred bring it close. This is worth seeing rather than being told, because it is the intuition behind why a run of bad luck in a game is unremarkable, and why small samples in any context are untrustworthy. The last twenty rolls are kept so you can see the streaks that feel impossible and are not.

Copying the result as text

The distribution is calculated in the page with ordinary integer arithmetic, and nothing you enter is transmitted, stored or logged. The summary line can be copied as text, which is convenient for pasting a result into game notes or a discussion about a rules question.

// Dice Probability Calculator: FAQ

What does notation like 3d6 mean?: The number before the d is how many dice, and the number after it is how many sides each has. So 3d6 is three six-sided dice, 1d20 is a single twenty-sided die, and 2d10 is two ten-sided dice. The total is the sum of the faces rolled.
Are the probabilities exact or simulated?: Exact. They come from counting every possible combination by convolution, not from sampling. The simulator is separate, and exists to show how observed frequencies converge on those exact values as the number of rolls grows.
Why is seven the most likely total on 2d6?: Because it has the most combinations. Six of the thirty-six equally likely outcomes sum to seven, against only one for two and one for twelve. The further a total is from the middle, the fewer ways there are to reach it, which is what produces the triangular shape.
How do I find the chance of rolling at least a certain total?: Set the comparison to at least and enter the target. The headline figure is the cumulative probability, and the table also shows a running cumulative column if you want to read several thresholds at once.
Why does the shape become a bell curve with more dice?: Because summing independent random values tends towards a normal distribution, which is the central limit theorem. With one die every outcome is equally likely; with several, middling totals have vastly more combinations than extreme ones, and the curve tightens as you add dice.
Does it handle modifiers, such as 2d6 plus 3?: Not directly, but the adjustment is simple: subtract the modifier from your target and ask the same question of the unmodified dice. Needing at least 10 on 2d6 plus 3 is the same as needing at least 7 on 2d6, which the tool answers directly.
What about advantage, or rolling several and keeping the highest?: Those mechanics are not sums, so they are outside what this calculator models. Rolling twice and keeping the better result has a different distribution from rolling once, and mechanics that drop the lowest of four dice need their own treatment. This tool covers the sum of N dice with M sides.
Why does my simulated result differ from the exact probability?: Because that is how randomness behaves at small sample sizes. Twenty rolls can easily land ten percentage points away from the true value; several hundred will usually be close. Watching the gap narrow is one of the more useful things the simulator does.
Can I use this for games other than tabletop RPGs?: Yes. Any question about the sum of several uniform random values has the same structure, whether it concerns a board game, a probability exercise or a sanity check on a simulation. The dice framing is just the most familiar way to express it.
Are the dice settings sent to a server?: No. The calculation and the simulation both run in your browser, and nothing you enter leaves the page.

// How to Use Dice Probability Calculator

Set the dice

Enter how many dice and how many sides each has. The range of possible totals appears beneath, which is a quick check that you have entered what you intended.
Choose a condition

Pick a comparison, such as at least or at most, and a target total. The headline probability updates immediately, so you can see what one more or one fewer point is worth.
Read the distribution, or roll

The chart and the table show every total with its combinations, probability and cumulative figure. Press the roll button to simulate the same dice and watch the observed frequency approach the exact value.

Category Utilities