Dice notation explained: how to read 2d6+3, d20, and friends
Dice notation is a short code for "how many dice, how many faces, what modifier." The string 2d6+3 means: roll two six-sided dice, add them, then add 3.
Once you can parse that pattern, almost every tabletop rulebook stops looking like a cipher. This guide defines the grammar, walks common examples (including D&D-style d20 checks), and shows where a digital roller helps when you do not have a full dice bag.
What dice notation means
The usual form is:
NdX±Y
| Part | Meaning | Example in 2d6+3 |
|---|---|---|
| N | How many dice to roll | 2 |
| d | Literal "die / dice" | d |
| X | Faces per die (1 through X, usually) | 6 |
| ±Y | Optional modifier after the sum | +3 |
Roll each die independently. Sum the face-up results. Apply the modifier last.
If N is omitted, it means one die: d20 = 1d20.
Worked examples
d6
One six-sided die. Outcomes 1–6, each equally likely if the die is fair. Classic board-game die.
2d6
Two six-sided dice, summed. Range 2–12. Distribution is not flat: 7 is the most common sum (six ways), 2 and 12 are rarest (one way each). That curve is why "roll 2d6" feels different from "roll 1d12."
2d6+3
Same as 2d6, then add 3. Range 5–15. The +3 shifts the whole curve up; it does not flatten it.
d20
One twenty-sided die. Outcomes 1–20. The backbone of many RPG attack rolls and ability checks.
4d6 drop lowest (character stats)
Common houserule / chargen method: roll four d6, discard the lowest, keep the sum of three. Notation sometimes written 4d6dl1 or described in words. Your roller must support "drop" explicitly; a plain 4d6 sum is not the same thing.
Advantage / disadvantage (d20)
In games that use it: roll 2d20, keep the higher (advantage) or lower (disadvantage). That is not written as 2d20+0 in the usual sum sense. It is a keep-high / keep-low rule on top of two rolls.
Standard polyhedral shorthand
| Notation | Faces | Typical use |
|---|---|---|
| d4 | 4 | Small damage, some spells |
| d6 | 6 | Damage, many board games |
| d8 | 8 | Medium damage |
| d10 | 10 | Damage, some percentile setups |
| d12 | 12 | Heavy weapon damage |
| d20 | 20 | Checks, attacks, saves |
| d100 / d% | 100 | Percentile (often 2d10 as tens + ones) |
d100 is often rolled as two d10s (tens digit + ones digit), reading 00 as 100 depending on the system. A single 100-face roller and a percentile pair are not always identical in UX, but both aim at a 1–100 range.
How to evaluate a roll string in your head
- Identify N and X.
- Know the min/max: min = N×1 ± Y, max = N×X ± Y (for simple sums with a constant modifier).
- Remember sums of multiple dice are bell-shaped, not flat.
- Apply game-specific keep/drop/reroll rules only if the text says so. Do not invent them from the bare
NdXstring.
Example: 3d8+2 → min 5, max 26, average somewhere near the middle of that range (about 15.5 before you obsess over exact expectation).
Digital rollers vs physical dice
Physical dice can be imperfectly weighted. Digital rollers sample a software RNG and map it onto 1…X.
For tabletop fun, either is fine if everyone at the table agrees on the tool. For a published raffle or anything with money on the line, process transparency matters more than whether the die is plastic or pixels. See coin flip vs dice vs RNG fairness and how to run a fair online raffle.
How to roll NdX±Y on this site
Open the dice roller:
- Set faces to X (presets include d4–d20 and d100).
- Set count to N.
- Set the modifier to Y (positive or negative).
- Roll. The tool sums the dice and applies the modifier.
Shortcuts for common faces: d20, d6, d100.
If you only need a flat integer from 1 to 20 with no tabletop framing, random 1 to 20 is the same outcome space as a single d20 without multi-die syntax.
FAQ
What does 2d6+3 mean?
Roll two six-sided dice, add the results, then add 3. Minimum 5, maximum 15.
What does d20 mean in D&D?
Usually one twenty-sided die. Ability checks, attack rolls, and saving throws often start with a d20, then add modifiers from your sheet.
Is 2d6 the same as 1d12?
No. Both max out near the same ballpark, but 2d6 clusters toward the middle and never rolls a 1. 1d12 is flat across 1–12.
Can I roll dice notation online without buying dice?
Yes. Use a multi-dice roller with modifiers, or preset pages like d20 and d6.
Disclaimer: Educational rules primer only. Game publishers define their own notation extensions (explode, keep, reroll). When a book disagrees with this guide, the book wins at that table. Our roller produces random personal rolls for play and practice; it does not replace official apps a publisher may require.