# DnD Dice Roller

URL: https://speedycalculator.com/calculators/statistics/dnd-dice-roller/
Last updated: 2026-10-30

> The DnD dice roller understands dice notation such as 1d20+5, 2d6+3, 8d6 or 4d6kh3, rolls several expressions at once, shows every die and result, and gives the exact average, range and probability chart for each roll – with quick presets for attacks, fireballs and ability scores.

## Inputs

- Roll
- Dice expression(s), separated by commas

## Results

- Result (first expression)
- Dice rolled (first expression)
- Sum of all expressions
- Average of the first expression
- Chance of rolling this result or higher
- All rolls
- Distribution of the first expression

## Formula

```
NdS + M: average = N(S + 1)/2 + M, range N + M to NS + M · 4d6kh3 (keep highest 3) averages 12.24 · 2d20kh1 = advantage
```

## Explanation

Dungeons & Dragons uses seven dice – d4, d6, d8, d10 (two of them for percentiles), d12 and d20 – and a compact notation to describe how to roll them. "2d6+3" means roll two six-sided dice and add 3; "8d6" is a fireball; "1d20+7" is an attack with a +7 bonus. Character creation often uses "4d6 drop lowest", written 4d6kh3: roll four d6s and keep the highest three.

This roller reads that notation directly. Type one or more expressions separated by commas – a whole turn's attack and damage, or six ability scores – and it rolls them all, showing the individual dice, the dice kept, each result, the exact average and the possible range. Supported forms include NdS, d% for a percentile die, plus and minus modifiers, combinations of dice such as 1d8+1d6+2, and keep or drop rules: kh (keep highest), kl (keep lowest) and d (drop lowest).

The chart shows the exact probability distribution of the first expression with your result highlighted, and the tool reports the chance of rolling your result or higher – handy for knowing just how lucky that 18 on 4d6kh3 was (about 1.6%).

### How to use the DnD Dice Roller

- **Roll**
- **Dice expression(s), separated by commas**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Each expression is parsed into dice groups and constants. Dice are rolled with the secure random generator; keep and drop rules sort the group and keep the requested dice. The exact distribution is built by enumerating keep-rule groups and convolving all the parts, which gives the exact average and the chart.

### Worked example

Rolling "1d20+5, 2d6+3": the attack came up 13 + 5 = 18 and the damage 4 + 6 + 3 = 13. The attack averages 15.5 (range 6–25) and the damage averages 10 (range 5–15). For 4d6kh3 the exact average is 15,869/1,296 ≈ 12.24, noticeably higher than the 10.5 of plain 3d6.

### Supported notation

You typeMeaningd20 or 1d20one twenty-sided die3d8+2three d8 plus 21d8+1d6+3mixed dice plus a modifierd%a percentile die (1–100)4d6kh3keep the highest 3 of 4d64d6d1drop the lowest 1 die2d20kl1disadvantage – keep the lower d20

## Worked example

Inputs — Roll: Type your own dice expression; Dice expression(s), separated by commas: 1d20+5, 2d6+3.

Results — **Result (first expression) = 8**; Dice rolled (first expression) = [3] + 5; Sum of all expressions = 18; Average of the first expression = 15.5; Chance of rolling this result or higher = 90 %; All rolls = Roll Dice Result Average Range
────────────────────────────────────────────────
1d20+5 [3] + 5 8 15.5 6 to 25
2d6+3 [2, 5] + 3 10 10 5 to 15.

## Key terms

- **Dice notation**: A shorthand such as 3d8+2: number of dice, d, number of sides, then modifiers.
- **Keep highest (kh)**: Roll several dice and keep only the highest ones, e.g. 4d6kh3.
- **Hit dice**: Dice used for hit points, e.g. d10 for fighters and d12 for barbarians.

## FAQ

**What does 2d6+3 mean?**
Roll two six-sided dice and add 3. It averages 10 and ranges from 5 to 15.

**How do I roll ability scores?**
Use 4d6kh3 six times (preset "Ability scores"): roll four d6, drop the lowest. Each score averages about 12.24.

**What dice are in a D&D set?**
d4, d6, d8, two d10s (one for tens), d12 and d20.

**How much damage does Fireball do?**
8d6 fire damage: 28 on average, 8 to 48, with a standard deviation of about 4.8.

**How do I write advantage in dice notation?**
2d20kh1 – roll two d20s and keep the highest. Disadvantage is 2d20kl1.

**What is the chance of rolling 18 on 4d6 drop lowest?**
21 of the 1,296 outcomes give 18, about 1.62%.

**Can I subtract dice?**
Yes, for example 1d8-1d4; the result can be negative.


## Sources

- [Wolfram MathWorld – Dice](https://mathworld.wolfram.com/Dice.html)
- [Penn State STAT 414 – Introduction to Probability Theory](https://online.stat.psu.edu/stat414/)