About Dice Notation
Dice notation — sometimes called dice algebra — is a compact shorthand for describing dice rolls. It dates back to early tabletop wargames and is now the universal language of tabletop RPGs, from Dungeons & Dragons and Pathfinder to Warhammer and Call of Cthulhu.
The format is XdY±Z: roll X dice, each with Y sides, then add or subtract Z from the total. Dice notation is compact, unambiguous and computable — which is why dice rollers, character sheets, virtual tabletops and random generators all speak it.
The standard polyhedral dice
| Die | Shape | Range | Common use |
|---|---|---|---|
| D4 | Tetrahedron | 1–4 | Daggers, magic missile, small weapons |
| D6 | Cube | 1–6 | Standard damage, most board games |
| D8 | Octahedron | 1–8 | Longswords, battleaxes, healing potions |
| D10 | Pentagonal trapezohedron | 1–10 | Percentage rolls, some weapons |
| D12 | Dodecahedron | 1–12 | Greataxes, barbarian weapons |
| D20 | Icosahedron | 1–20 | Attack rolls, skill checks, saves |
| D100 | Percentile (two D10s) | 1–100 | Random tables, critical hit location |
Common dice notation examples
| Notation | Meaning | Range |
|---|---|---|
| 1d20 | One twenty-sided die | 1–20 |
| 3d6 | Three six-sided dice, summed | 3–18 |
| 2d20+5 | Two d20s, add 5 to the total | 7–45 |
| 1d8+3 | Longsword damage with +3 bonus | 4–11 |
| 8d6 | Fireball damage at 3rd level | 8–48 |
| 1d100-10 | Percentile with a −10 penalty | −9–90 |
| 4d6-1 | Four d6s, subtract 1 | 3–23 |
Interpreting the results
When you roll 3d6+2, the tool shows:
- Each die individually — three values in the range 1–6, displayed as physical dice faces.
- The sum of the dice — for example 4 + 2 + 6 = 12.
- The modifier — added to produce the final total (12 + 2 = 14).
- The total — the final result the game cares about.
Individual dice matter when your game has mechanics that depend on individual results, such as critical hits (a natural 20 on a d20), fumbles (a 1), or abilities that reroll the lowest die.
What makes a "critical" roll?
In D&D 5e, a natural 20 on an attack roll is a critical hit — double damage dice. A natural 1 on an attack roll is an automatic miss. In other systems the thresholds vary. This tool highlights max-value results on each die when "Highlight critical rolls" is enabled, so you can spot them at a glance.
Note that the natural 20 / natural 1 mechanic only applies to a single d20 roll, not to a sum. A 6 on one of the three d6s in 3d6+2 is not a critical — only the total matters.
Common use cases
Tabletop RPGs
D&D, Pathfinder, Call of Cthulhu, Warhammer.
Board games
Roll for movement, combat resolution, chance.
Random selection
Pick numbers for draws and games.
Simulation
Model dice-based systems and probability.
Teaching probability
Show how dice distributions work in real time.
Prototyping
Test game mechanics before you build them.
Privacy
This dice roller runs entirely in your browser. Every roll uses Math.random() locally, and your roll history is stored only in your browser's localStorage. Nothing is transmitted, stored or logged on any server. Clear your browser data and the history is gone.