20-sided D20 dice simulator for D&D attack rolls, saving throws, and initiative with 5.00% odds
Need a standard 6-sided die? Roll our 1 to 6 dice roller or return to our master random number generator wheel for 1-100 percentile ranges.
| Slice Segment Name | Assigned Weight | Calculated Odds (%) | Fractional Odds | Angular Span |
|---|---|---|---|---|
| D20 (1) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (2) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (3) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (4) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (5) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (6) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (7) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (8) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (9) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (10) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (11) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (12) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (13) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (14) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (15) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (16) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (17) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (18) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (19) | 1 | 5.00% | 1 in 20.0 | 18.0° |
| D20 (20) | 1 | 5.00% | 1 in 20.0 | 18.0° |
Pick a number between 1 and 20 with an exact 5.00% (1/20) uniform probability per sector, engineered for D&D D20 dice checks and tabletop RPG campaigns.
Pick a number between 1 and 20 with provable cryptographic fairness. The 1 to 20 Wheel functions as a digital 20-sided D20 die, delivering an exact 5.00% uniform mathematical probability across its twenty 18-degree sectors for Dungeons & Dragons, Pathfinder, and tabletop RPG campaigns.
The randomization architecture behind Pick a Number 1 to 20 Wheel (D20) follows a deterministic multi-stage evaluation pipeline to ensure complete unpredictability and uniform probability distribution:
The 360° circle is divided into twenty 18° sectors representing D20 faces 1 through 20.
A 32-bit integer is drawn from the OS entropy pool and mapped via X = 1 + (R mod 20).
Deceleration lands on the winning face, spotlighting Nat 20 criticals with confetti fanfare.
For X ~ U{1, 20}, the discrete uniform probability mass function satisfies P(X = k) = 0.05 for all k in {1, 2, ..., 20}. Expected value E[X] = 10.50 and variance Var(X) = 33.25. The probability of rolling a critical hit (X = 20) or critical fumble (X = 1) is identically 1/20 = 5.00%.
Where P(E_i) denotes the probability of landing on segment i, w_i represents the assigned discrete integer weight, and θ_i represents the continuous angular arc length in radians.
Physical D20 dice often have internal air bubbles and face-rounding imperfections. CSPRNG digital dice ensure exact 5.00% uniform odds across every face.
Rolling attack rolls, ability checks, saving throws, and initiative order.
Randomizing 20-tier plot events and character encounter tables.
Direct answers to questions regarding D&D tabletop rules, critical rolls, and D20 probability
Yes. The 1 to 20 Wheel partitions the 360-degree circle into 20 equal 18.0-degree sectors (pi/10 radians), delivering an authentic, unbiased 5.00% probability for critical hits (Nat 20) and critical fumbles (Nat 1).
Yes. The 120 FPS animated spin with celebratory chime fanfare provides immersive visual suspense for Discord, Twitch, and YouTube D&D campaigns.
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