Dice Roller
Roll virtual dice from D4 to D20 with modifiers. Uses cryptographically secure random values. Beautiful animated SVG dice faces — perfect for D&D, tabletop RPGs, and board games.
Dice Roller
Results update instantly as you type
Enter Values
Average Roll
4.0
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Total Roll
8
D4 × 2
Individual Rolls
4, 4
Dice
D4 × 2
Modifier
+0
Average
4.0
The Formula
Each die roll is a uniformly distributed random integer between 1 and the number of sides. The total is the sum of all individual rolls, plus any flat modifier (bonus or penalty). Dice notation is commonly written as NdS+M, where N = number of dice, S = sides per die, and M = modifier. For example, 2D6+3 means roll two six-sided dice, sum them, and add 3. The average result is N × (S+1)/2 + M.
Variable Definitions
Dice Count & Sides
N dice, each with S sides (D4, D6, D8, D10, D12, D20). More dice produce a tighter bell curve around the average.
Modifier
A flat bonus (positive) or penalty (negative) added to the total after summing all dice. In D&D, this often represents ability score modifiers or proficiency bonuses.
Average Result
The expected value: N × (S + 1) / 2 + M. For a single D6, average is 3.5. For 2D6, average is 7. For 2D6+3, average is 10.
How to Use This Calculator
- 1
Choose how many dice to roll (1 to 10 dice per roll).
- 2
Select the die type from the dropdown: D4, D6, D8, D10, D12, or D20.
- 3
Optionally add a modifier (e.g., +5 for a proficiency bonus, or -2 for a penalty).
- 4
Click calculate to see individual die results, the total sum, and the average expected value.
- 5
The dice are displayed visually — pip patterns for D6 and numeric faces for other dice types.
Rolling two six-sided dice creates a triangular distribution where 7 is the most likely outcome (1-in-6 chance).
Understanding the Concept
Dice rolling is fundamental to tabletop role-playing games (TTRPGs) like Dungeons & Dragons, as well as board games, war games, and probability simulations. Each die produces a uniformly distributed random integer. For a fair S-sided die, every face has a 1/S probability of appearing. The sum of multiple dice approximates a normal distribution due to the Central Limit Theorem — the more dice you roll, the more the results cluster around the average in a bell curve shape. The average roll of a single die is (S + 1) / 2, so 2D6 averages 7, and 2D6+3 averages 10. All rolls use crypto.getRandomValues() for cryptographically secure randomness, which is superior to the default Math.random() for gaming applications where fair results matter.
Frequently Asked Questions
Sources & References
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