A D20 Probability Calculator is a tool used by tabletop role-playing game (TTRPG) enthusiasts, mathematicians, and probability analysts to determine the likelihood of rolling specific results on a 20-sided die (d20). This is particularly useful in games like Dungeons & Dragons (D&D), where dice rolls influence combat, skill checks, and saving throws.
By using this calculator, players and game masters can:
- Determine the probability of rolling a specific number.
- Calculate the odds of rolling above or below a certain value.
- Assess chances of rolling within a specific range.
- Optimize game strategies by understanding roll probabilities.
Formula of D20 Probability Calculator
The probability of rolling any particular number on a fair d20 die is:
P(Outcome) = 1 / 20
This means each face (1 to 20) has an equal probability of 5% (0.05 or 1 in 20).
Calculating Other Probabilities
1. Probability of Rolling a Number Greater than or Equal to X:
If you want to calculate the probability of rolling a number greater than or equal to X, use the formula:
P(≥ X) = (21 – X) / 20
Example: Probability of rolling a 15 or higher:
P(≥ 15) = (21 – 15) / 20 = 6 / 20 = 0.30 or 30%
2. Probability of Rolling Less Than or Equal to X:
For rolling a number less than or equal to X, use:
P(≤ X) = X / 20
Example: Probability of rolling 10 or less:
P(≤ 10) = 10 / 20 = 0.50 or 50%
3. Probability of Rolling a Range of Numbers:
To calculate the probability of rolling within a specific range (e.g., between 5 and 15, inclusive):
P(5 ≤ X ≤ 15) = (15 – 5 + 1) / 20 = 11 / 20 = 0.55 or 55%
D20 Probability Reference Table
The following table provides common d20 probability calculations for quick reference.
| Roll Condition | Probability Formula | Probability (%) |
|---|---|---|
| Rolling a 1 | 1/20 | 5% |
| Rolling a 10 | 1/20 | 5% |
| Rolling 15+ | (21 – 15)/20 | 30% |
| Rolling 5 or less | 5/20 | 25% |
| Rolling 10-15 | (15-10+1)/20 | 30% |
| Rolling an even number | 10/20 | 50% |
This table is useful for players who want to quickly estimate probabilities without manually calculating each time.
Example of D20 Probability Calculator
Imagine a Dungeons & Dragons player needs to roll a 17 or higher to land a successful attack. Using the formula:
P(≥ 17) = (21 – 17) / 20 = 4 / 20 = 0.20 or 20%
This means the player has a 20% chance of rolling 17 or higher on a d20.
Most Common FAQs
In most TTRPGs like D&D, rolling a natural 20 is an automatic success (critical hit), and rolling a natural 1 is an automatic failure (critical failure). The probability of rolling a critical success or failure is always 5%.
Since the probability of rolling a 20 is 1/20, the probability of rolling two consecutive 20s is: (1/20) × (1/20) = 1/400 = 0.0025 or 0.25%
Yes, modifiers (bonuses or penalties) shift the effective success rate but do not change the actual probability of rolling any given number. For example, if a character has a +5 modifier, then rolling a 15 or higher effectively counts as rolling a 10 or higher before modifiers.