Expert in TTRPG mathematical modeling and probability analysis.
Optimize your combat strategy with our professional D&D Dice Calculator. Whether you are calculating average damage for a Fireball or determining the probability of hitting a high AC boss, this tool provides precise mathematical expectations for Dungeons & Dragons 5e and other D20 systems.
D&D Dice Calculator
D&D Dice Calculator Formula:
Average Damage (EV) = N × ((D + 1) / 2) + M
Success Prob. (P) = [21 – (DC – M)] / 20 (for d20)
Formula Source: Wizards of the Coast – Official Rules & AnyDice Probability Logic
Variables:
- Number of Dice (N): The quantity of dice rolled (e.g., the ‘8’ in 8d6).
- Dice Sides (D): The type of die used (d4, d6, d8, d10, d12, d20).
- Modifier (M): Static bonuses from ability scores, proficiency, or magic items.
- Target DC: The Difficulty Class or Armor Class you must meet to succeed.
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What is a D&D Dice Calculator?
A D&D Dice Calculator is a mathematical tool designed for players and Dungeon Masters of tabletop roleplaying games like Dungeons & Dragons and Pathfinder. It calculates the statistical expected value (average) of any dice roll combination, helping you understand how much damage your character is likely to deal over time.
Beyond simple averages, this calculator can determine the probability of success against a specific Target DC (Difficulty Class). This is essential for evaluating whether using features like “Great Weapon Master” or “Sharpshooter” is statistically advantageous against specific enemy AC.
How to Calculate D&D Dice Rolls (Example):
- Identify the dice string (e.g., 2d8 + 5).
- Find the average of the die type: (8 + 1) / 2 = 4.5.
- Multiply by the number of dice: 2 × 4.5 = 9.
- Add your flat modifier: 9 + 5 = 14. Your average damage is 14.
Frequently Asked Questions (FAQ):
How do you calculate the average of a d6? The average is 3.5. This is calculated by (1+6)/2.
Does this calculator account for Advantage? This base tool calculates flat rolls. Advantage typically increases the average d20 roll from 10.5 to 13.82.
Why is my average damage not a whole number? Dice averages often end in .5 because they represent the long-term mathematical mean, not a single roll result.
What is the maximum for 3d10 + 7? The maximum is (3 × 10) + 7 = 37.