Custom Dice Roller
Roll up to 15 fair virtual dice with mixed side counts, inspect each outcome, and export the current roll as a validated Excel workbook.
Dice setup
Required. Choose 1 to 15 dice.
Optional shortcut. Select one die type to apply it to every active die.
Individual dice
20 supported die types, from d2 to d120Current roll
Roll details
| Die | Sides | Roll | Expected value |
|---|---|---|---|
| Die 1 | 6 | 4 | 3.50 |
| Die 2 | 8 | 7 | 4.50 |
| Die 3 | 10 | 9 | 5.50 |
| Die 4 | 20 | 13 | 10.50 |
How to use this custom dice roller
What this calculator does
This tool simulates a roll of one to fifteen independent fair dice. Each die can use a different number of sides, so a single roll can combine familiar tabletop dice such as d6, d8, d10, d12, and d20 with less common choices up to d120. The calculator reports the actual random roll, its sum, the mathematically possible total range, and the expected total for the selected dice. It is a simulation and probability aid: it does not determine whether a physical die is balanced, predict future random outcomes, or model loaded dice.
When to use it
Use the roller when you need replacement dice for a board or role-playing game, when a rule asks for a mixed pool such as d6 + d8 + d20, when you want to demonstrate how different die sizes change the range and average of a sum, or when you need a compact record of a roll that can be exported to Excel. For background on browser-generated random values, see the MDN guide to Crypto.getRandomValues().
How to calculate
- The calculator opens with a ready-to-use demonstration: 4 dice configured as d6, d8, d10, and d20, with the sample roll 4, 7, 9, and 13. The first-open total is 33, and the example Excel workbook is immediately available.
- Choose Number of dice from 1 to 15. Changing the active count rebuilds the individual dice list and immediately produces a fresh valid roll for that configuration.
- Use Set all dice types to when every active die should have the same number of sides. Keep Mixed / custom when the dice differ.
- For a mixed pool, choose each Die 1 sides through Die 15 sides value as needed. The active list only shows the dice currently in use. Each die is required and must use one of the supported d2 – d120 options.
- Press Roll dice whenever you want a new random outcome without changing the setup. Read Total, Expected total, Possible total, Dice rolled, Rolled values, and the Roll details table.
- Use Download Excel to export the current setup and exact current roll. Reset intentionally clears the demonstration and active dice; after reset, Excel export is disabled until you choose a complete valid setup again.
Input guide
Number of dice is a required integer choice from 1 to 15; the startup example uses 4. More dice raise the minimum possible total by one per added die and usually increase both the maximum and expected total. A common mistake is assuming “more dice” changes the sides of existing dice; it only changes how many independent dice are rolled.
Set all dice types to is an optional shortcut. Choose Mixed / custom, or one supported side count such as d6. Selecting d6 makes every active die a six-sided die; changing an individual die afterward returns the shortcut to Mixed / custom.
Die 1 sides through Die 15 sides are required categorical choices for active dice. Each choice is a positive whole-number face count from the provided set. A d20, for example, can return any integer from 1 to 20. Higher side counts increase that die's maximum and expected value. Do not enter percentile notation such as “00”; use the explicit d100 option instead.
Output guide
Total is the exact sum of the current simulated outcomes. Expected total is the sum of each die's long-run mean and can be fractional even though every actual roll is an integer. Possible total shows the exact minimum and maximum sum for the selected dice. Dice rolled confirms the active count. Rolled values lists the current outcomes in die order.
The Roll details table has four columns: Die identifies the position; Sides gives that die's face count; Roll is the current random result; and Expected value is the exact mean (N + 1) / 2 for a fair dN. A high or low individual roll is not evidence of bias by itself; randomness naturally includes streaks and extremes.
Worked example
The startup pool is d6 + d8 + d10 + d20. Its shown sample outcomes are 4 + 7 + 9 + 13, so the displayed Total is 33. The smallest possible total is 1 + 1 + 1 + 1 = 4, while the largest is 6 + 8 + 10 + 20 = 44, so Possible total is 4 – 44. For a fair dN, the expected value is (N + 1) / 2. Therefore the four means are 3.5, 4.5, 5.5, and 10.5, which sum to the displayed Expected total of 24.00. The expected total describes a long-run average across many rolls; it does not mean 24 is the most likely or guaranteed next sum.
How are fair dice values generated?
A fair die assigns equal probability to each integer face from 1 through N. This calculator draws browser random integers and uses rejection sampling when the browser exposes a strong random-value source, which avoids the small modulo bias that can occur when a fixed-size integer range is not evenly divisible by the number of die faces. The NIST recommendation on deterministic random bit generators provides background on the design of high-quality random-bit generators. For the broader statistical idea of equal probability across a range, the NIST Engineering Statistics Handbook discussion of the uniform distribution explains why uniform random numbers are a foundational reference model.
For each selected dN, the possible values are the integers 1, 2, ..., N. The exact minimum of a multi-die sum is therefore the number of dice, because every die can show 1. The exact maximum is the sum of all selected side counts. Linearity of expectation lets the calculator add individual die means even when the dice have different sizes. No chart is needed for a single realized roll because a table communicates the discrete outcomes and unlike die ranges more directly without suggesting that one random snapshot is a stable distribution.
How should you interpret a single roll?
A single result is one sample, not a probability estimate. Rolling a d20 and getting 20 is unusual on that one die, but it is still a valid fair outcome with probability 1/20. Likewise, a mixed-dice total far above or below the expected total can occur naturally. If you need to study the distribution of totals, you would normally repeat the experiment many times or compute the exact convolution of the dice distributions. This calculator intentionally focuses on the current roll and its exact range and expectation rather than presenting a chart from one observation.
Changing a die from d6 to d20 increases its maximum by 14 and increases its expected value from 3.5 to 10.5. Adding another die raises the minimum total by 1 and raises the maximum by that die's side count. These relationships are deterministic even though the current roll itself is random, which makes the range and expected value useful checks when reviewing game rules or teaching basic probability.