Is this a simulation or exact math?

It is exact. The tool convolves the uniform distribution of each die into a full distribution of every possible total, then counts favorable outcomes. There is no randomness or sampling error, so 2d6 totaling 7 reports exactly 6 in 36, or 16.67%.

How is the modifier applied?

A flat modifier shifts every possible total by that amount. Rolling 1d20+5 simply moves the d20 range from 1-20 to 6-25, so the probabilities are identical to a d20 with the target lowered by 5.

What does expected (mean) total mean?

It is the average total you would get over many rolls, equal to the sum of each outcome weighted by its probability. For a single fair die it is the midpoint, so a d6 averages 3.5 and 2d6 averages 7.

Can I mix different dice together?

Yes. You can combine any counts of d4, d6, d8, d10, d12, d20, and d100. The calculator builds the combined distribution exactly, which is useful for damage rolls like 1d8 plus 2d6 sneak attack.

Why does adding many large dice feel slow?

The number of possible totals grows with the dice, especially d100s. The math stays exact, but extreme pools have a very wide range. Keeping counts reasonable, the way real D&D rolls work, keeps results instant.

D&D Dice Probability Calculator

Get the true odds of any D&D roll. Enter a pool of dice, an optional modifier, and a target, and this calculator returns the exact probability of hitting it, plus the full range and average. No simulation and no guesswork, just precise tabletop math in your browser.

How it works

Each fair die is a uniform distribution: a d6 has outcomes 1-6 each equally likely. To find the distribution of a sum like 2d6 + 1d8, the tool convolves the dice one at a time, building a table that maps every possible total to the number of equally-likely outcomes that produce it.

For 2d6, there are 6 × 6 = 36 outcomes; a total of 7 happens 6 ways, so P(7) = 6/36 ≈ 16.67%. A flat modifier simply shifts every total. The probability for your comparison is then:

P = (favorable outcomes) / (total outcomes)

The expected (mean) total is the sum of each possible total multiplied by its probability.

Tips and example

To find your chance to hit, set the pool to a single d20, add your attack bonus as the modifier, use at least, and set the target to the enemy’s Armor Class.
For damage, combine the weapon dice (say 1d8) with extras (2d6 sneak attack) and read the expected mean to compare builds.
“At most” is handy for checking failure odds, such as the chance a saving throw misses a DC.
Because the math is exact, the favorable-over-total count shows you the underlying fractions, not a rounded estimate.