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.

What is the D&D Dice Probability Calculator?

Calculate the exact probability of rolling at least, at most, or exactly a target total on any combination of D&D dice (d4, d6, d8, d10, d12, d20, d100) plus a modifier. For 5e players and GMs assessing odds and encounter difficulty. It runs free in your browser on Gera Tools, with nothing uploaded.

D&D Dice Probability Calculator

Name: D&D Dice Probability Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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.

Common D&D probability questions answered

Why do more dice make your total more predictable?

A single d6 is equally likely to show any value from 1 to 6. Roll ten d6 and the total clusters tightly around 35 — the distribution of totals is bell-shaped, and extreme results become rare. This is the central limit theorem at work: each extra die adds its own independent variation, but because they average out, the whole pool becomes more predictable. In D&D terms, this is why a 1d20 attack roll has wild swings (any result is equally likely) while a 2d6 damage roll almost always produces middle values (7 is the most common result, roughly 17% of the time, and extremes are rare).

Understanding “at least” vs. “at most” vs. “exactly”

These three comparisons answer different questions:

At least X answers “do I succeed?” for target-based rolls. Roll at least 14 to hit AC 14.
At most X answers “do I fail or stay below a limit?” Can also represent “at most X rounds of duration before a recharge.”
Exactly X answers specific questions like “what is the chance I roll exactly 7 on 2d6?” It is rarely the most useful comparison for gameplay but is interesting for statistical analysis.

For damage rolls, “at least X” tells you the probability of dealing a minimum threshold, useful for checking whether a killing blow is possible.

Expected damage and build comparisons

The expected (mean) total is the most useful single number for comparing weapon or spell choices. For example:

A greatsword deals 2d6 damage, average 7 per hit.
A greataxe deals 1d12, also average 6.5 per hit — slightly lower.
A fighter with Great Weapon Fighting rerolls 1s and 2s, raising the expected value.

The greatsword wins on average, but the greataxe has a higher peak (12 vs. 12 — tied) and a lower floor (1 vs. 2). For a character who wants consistent output, the greatsword is mathematically preferable. For dramatic flair, the greataxe offers an equal chance of the maximum. This calculator shows the full distribution so you can make that trade-off consciously.

Saving throws and concentration checks

When a Wizard concentrating on Hold Person takes 25 damage, they must make a Constitution saving throw against DC 13 (half the damage taken, minimum 10). If the Wizard has a +2 Constitution modifier and proficiency (+3 at level 5), their save bonus is +5. Use the calculator: 1d20, modifier +5, comparison “at least 13”, to find the exact chance of maintaining concentration. At modifier +5, reaching DC 13 needs an 8 or better on the die — about 65%.