If provided, notation will auto-fill the fields below.
What this average dice calculator does
This tool calculates the expected value (average) of a dice roll, plus useful supporting values: minimum roll, maximum roll, and optional probability of hitting a target number. It works for common tabletop formats like 1d20, 2d6+1, 4d8-2, and more.
If you have ever asked, “Is 3d4 better than 1d12?” or “What is the average damage of 2d6+3?” this calculator gives a fast, reliable answer.
How to use it
Option 1: Enter dice notation
Type a standard expression like 3d6+2 and click Apply Notation. The form fields update automatically.
Option 2: Fill in fields directly
- Number of dice (for example, 2)
- Sides per die (for example, 6)
- Modifier (for example, +3 or -1)
- Target total (optional; use this to compute chance of rolling at least that amount)
The core formula
The average of one fair die with S sides is:
(S + 1) / 2
For N dice and modifier M:
Average total = N × (S + 1) / 2 + M
Example: for 2d6+3, the average is:
2 × (6 + 1) / 2 + 3 = 10
Average vs. probability: an important distinction
Average does not mean “most common” in every case. A d20 averages 10.5, but each face has the same 5% chance. With multiple dice, center values become more likely (a bell-shaped pattern). That is why 2d6 feels more consistent than 1d12, even though both can reach 12.
- 1d12: flat distribution (all outcomes equally likely)
- 2d6: middle totals (6, 7, 8) are more frequent
- Practical effect: multi-die systems reduce wild swings
Why this matters for RPGs and game balance
Damage planning
If your attack says 3d8+4, knowing the expected value helps estimate damage per round and compare weapons or spells.
Encounter tuning
Game masters can use averages to check whether enemy health, player damage, and fight length feel appropriate.
Build optimization
Players can compare abilities objectively. Sometimes a smaller die pool with a strong modifier beats a larger pool with no bonus.
Quick examples
- 1d20: average 10.5
- 2d6: average 7
- 4d6: average 14
- 2d10+5: average 16
- 8d6-2: average 26
Frequently asked questions
Can I use negative modifiers?
Yes. Enter a negative number (for example, -2), or use notation like 3d6-2.
Is target probability exact?
For typical input sizes, the calculator uses exact distribution math. For very large combinations, it switches to a normal approximation to keep calculations fast.
Does this support d100 and unusual dice?
Yes. Any fair die with 2 or more sides is supported, including d4, d8, d10, d12, d20, d100, and custom side counts.
Final thought
Dice are random, but strategy does not have to be. Use average values and target probabilities to make better decisions, build better encounters, and understand your game math with confidence.