Dice notation
2d20
Roll 2d20 and see where it lands on the real distribution. Range 2 to 40, averaging 21.00.
The shape of 2d20
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 2
- Highest
- 40
- Average
- 21.00
- Most likely
- 21
- Chance of 21
- 5.0%
- Possible totals
- 39
Peak at 21 (5.0%). Average 21.00. Range 2–40.
There is exactly one way to roll 2 and one way to roll 40, so each sits at 0.250%, or 1 in 400. There are 20 ways to make 21, which is why the middle of the range dominates. Rolling 2 dice instead of one trades range for reliability.
Every total, with odds
Exact figures, enumerated rather than simulated.
| Total | Chance | Odds | This or higher |
|---|---|---|---|
| 2 | 0.250% | 1 in 400 | 100.0% |
| 3 | 0.500% | 1 in 200 | 99.8% |
| 4 | 0.750% | 1 in 133 | 99.2% |
| 5 | 1.00% | 1 in 100 | 98.5% |
| 6 | 1.25% | 1 in 80 | 97.5% |
| 7 | 1.50% | 1 in 67 | 96.2% |
| 8 | 1.75% | 1 in 57 | 94.8% |
| 9 | 2.00% | 1 in 50 | 93.0% |
| 10 | 2.25% | 1 in 44 | 91.0% |
| 11 | 2.50% | 1 in 40 | 88.8% |
| 12 | 2.75% | 1 in 36 | 86.2% |
| 13 | 3.00% | 1 in 33 | 83.5% |
| 14 | 3.25% | 1 in 31 | 80.5% |
| 15 | 3.50% | 1 in 29 | 77.2% |
| 16 | 3.75% | 1 in 27 | 73.8% |
| 17 | 4.00% | 1 in 25 | 70.0% |
| 18 | 4.25% | 1 in 24 | 66.0% |
| 19 | 4.50% | 1 in 22 | 61.8% |
| 20 | 4.75% | 1 in 21 | 57.2% |
| 21 | 5.00% | 1 in 20 | 52.5% |
| 22 | 4.75% | 1 in 21 | 47.5% |
| 23 | 4.50% | 1 in 22 | 42.8% |
| 24 | 4.25% | 1 in 24 | 38.2% |
| 25 | 4.00% | 1 in 25 | 34.0% |
| 26 | 3.75% | 1 in 27 | 30.0% |
| 27 | 3.50% | 1 in 29 | 26.2% |
| 28 | 3.25% | 1 in 31 | 22.8% |
| 29 | 3.00% | 1 in 33 | 19.5% |
| 30 | 2.75% | 1 in 36 | 16.5% |
| 31 | 2.50% | 1 in 40 | 13.8% |
| 32 | 2.25% | 1 in 44 | 11.2% |
| 33 | 2.00% | 1 in 50 | 9.00% |
| 34 | 1.75% | 1 in 57 | 7.00% |
| 35 | 1.50% | 1 in 67 | 5.25% |
| 36 | 1.25% | 1 in 80 | 3.75% |
| 37 | 1.00% | 1 in 100 | 2.50% |
| 38 | 0.750% | 1 in 133 | 1.50% |
| 39 | 0.500% | 1 in 200 | 0.750% |
| 40 | 0.250% | 1 in 400 | 0.250% |
Common questions about 2d20
What is the average of 2d20?
21.00. The range runs 2 to 40, but the average sits in the middle because there are far more ways to land near the centre than at either end.
What are the odds of rolling 40 on 2d20?
0.250%, or 1 in 400. The minimum of 2 is equally rare at 0.250%. Both extremes need every die to cooperate.
What is the most likely result of 2d20?
21, at 5.0%. There are 20 different combinations that add up to 21, against 1 for 40. That gap is what makes the curve.
Is 2d20 the same as picking a number between 2 and 40?
No, and this is the most useful thing to understand about dice. Picking at random from 2 to 40 gives every one of those 39 results an equal 2.56% chance. 2d20 covers the same span with a hump in the middle: 21 lands 20 times more often than 40 does. Same range, completely different behaviour.