Dice Roller
Quickly find your Random dice rolls with our free Dice Roller. Simple, fast, and accurate.
Dice
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What is a Dice Roller Calculator?
A Dice Roller simulates rolling one or more dice of various sizes using cryptographically secure random number generation. It supports standard polyhedral dice (d4, d6, d8, d10, d12, d20, d100) used in tabletop role-playing games like Dungeons & Dragons, wargaming, and educational probability experiments. The roller displays each individual die result and the total sum.
How to calculate dice roll probability (the formula)
For a single die with s sides, each outcome has probability 1/s. The expected value is (s + 1) / 2. For the sum of n dice, the expected value is n × (s + 1) / 2. The distribution approaches a normal distribution as n increases (Central Limit Theorem). For example, the sum of two d6 (2d6) ranges from 2 to 12, with 7 being the most likely outcome (16.67% probability).
Example calculation
Roll 3d6 (three 6-sided dice). Possible outcomes: 3 to 18. The most common total is 10 or 11 (12.5% each). The probability of rolling a total of 10 is 27 / 6^3 = 27 / 216 ≈ 12.5%. A sample roll: [4, 2, 6] = total 12. The expected value for 3d6 is 3 × 3.5 = 10.5. Rolling with advantage (D&D, take the higher of two d20 rolls) has a 39.1% chance of rolling 15 or higher vs. 30% for a single d20.
Common mistakes
- Assuming dice outcomes are not independent — Each die roll is independent. The result of one die does not affect another, even when rolled together.
- Misunderstanding advantage/disadvantage probability — Advantage is not simply +5 to the roll. It shifts the probability curve significantly: the average d20 roll with advantage is 13.8 vs 10.5 normally.
- Confusing "3d6" with "d18" — 3d6 sums three independent dice (range 3-18) with a bell-shaped distribution centered on 10.5, while d18 would be a uniform distribution (equal probability for each value 1-18).
Frequently asked questions
What dice sizes are available?
Common sizes include d4, d6, d8, d10, d12, d20, and d100 for various games and simulations.
Can I roll multiple dice at once?
Yes, enter the number of dice (up to 100) and the roller will show each individual outcome and the total sum.
Are the dice rolls truly random?
Yes, the roller uses cryptographically secure random number generation for fair results.
What is a d20 used for?
The 20-sided die (d20) is the primary die used in Dungeons & Dragons and other tabletop RPGs for skill checks and combat.
How do you calculate the probability of a dice roll?
Each outcome has an equal 1/sides probability. The expected value is (sides + 1) / 2 per die.
What does 3d6 mean?
It means roll three 6-sided dice and sum the results, commonly used in RPG character stat generation.