D20 Roller
A D20 is a twenty-sided polyhedral die shaped like an icosahedron, generating numbers from 1 to 20 with an equal 5.00% probability per face.
âš™ Advanced Expression (NdM±K) â–¼
Saved Presets
Roll History
0Exact Mathematical Probability
Combinatorial EngineCalculates discrete binomial distributions, probability density, and cumulative odds for the active dice expression.
View Full Probability Table & Combinations â–¼
| Total | Ways | Exact % | ≥ At Least | ≤ At Most |
|---|
Roll N Times (Multi-Trial Simulation)
Execute up to 10,000 repeated trials to calculate empirical distributions and statistics.
Empirical Frequency Table
| Roll Total | Hits (Count) | Frequency Bar | Percentage |
|---|---|---|---|
| Click "Run Trials" to simulate rolls and generate frequency data. | |||
About the D20 (Regular Icosahedron)
The D20 is the definitive die of modern tabletop roleplaying systems (the d20 System). It resolves virtually all core action attempts: attack rolls, skill checks, ability checks, and saving throws. A natural 20 is typically celebrated as a critical hit, while a natural 1 is a critical failure.
Geometric Properties
Regular icosahedron featuring 20 equilateral triangular faces, 12 vertices, and 30 edges. Opposite faces always sum to 21 on standard gaming dice.
Common Tabletop & Gaming Uses
- • Attack rolls to determine if a weapon or spell hits target AC
- • Saving throws to resist spells, poisons, and environmental hazards
- • Skill checks: Perception, Stealth, Athletics, Persuasion, Arcana
- • Initiative rolls determining combat turn order
D20 Probability Basics
Every outcome from 1 through 20 has exactly a 5.00% chance. With Advantage (2D20 keep highest), the probability of rolling 15+ jumps from 30% to 51%.
| Face Value | Theoretical Odds | Exact Percentage |
|---|---|---|
| 1 | 1/20 | 5.00% |
| 5 | 1/20 | 5.00% |
| 10 | 1/20 | 5.00% |
| 15 | 1/20 | 5.00% |
| 20 | 1/20 | 5.00% |