What Is the Custom Dice Roller Calculator?
The Custom Dice Roller Calculator simulates rolling any number of dice with any number of sides — perfect for tabletop role-playing games like Dungeons & Dragons, board games, or any situation where you need a random result. Enter how many dice to roll, how many sides each die has, and an optional flat modifier, and the tool returns a live roll plus the theoretical minimum, maximum, and average outcome.
How to Use It
Set Number of dice (\(n\)), Sides per die (\(s\)), and an optional Modifier that is added to the total. For example, the classic "3d6+2" means roll three six-sided dice and add 2. Click calculate to get a fresh random total. Reload to roll again.
The Formula Explained
Each die is rolled with floor(random() × s) + 1, which yields a uniform integer from 1 to \(s\). The total is the sum of all \(n\) dice plus the modifier:
$$\text{Total} = \sum_{i=1}^{\text{Dice}} \left( \lfloor \text{rand} \times \text{Sides} \rfloor + 1 \right) + \text{Modifier}$$
The predictable statistics are: $$\begin{aligned} \text{Min} &= \text{Dice} + \text{Modifier} \\[0.4em] \text{Max} &= \text{Dice} \times \text{Sides} + \text{Modifier} \\[0.4em] \text{Avg} &= \text{Dice} \times \frac{\text{Sides} + 1}{2} + \text{Modifier} \end{aligned}$$
Worked Example
For 3d6+2: minimum \(= 3 + 2 = 5\), maximum \(= 3 \times 6 + 2 = 20\), average \(= 3 \times (6+1)/2 + 2 = 10.5 + 2 = 12.5\). Any single roll lands somewhere between 5 and 20, clustering near 12.5.
FAQ
Are the rolls truly random? They use a pseudo-random generator, which is statistically uniform and fine for games but not cryptographic use.
Why does my total change each time? Each calculation produces a new random roll. The min, max, and average shown are fixed properties of your dice setup.
Can I use it for d20 or d100? Yes — set sides to 20 or 100. Any positive whole number of sides works.
