Dice Combination Sheet
Enter any dice notation and get the full probability breakdown — every outcome, its odds, and a distribution chart.
| Sum | Combinations | Probability | Cumulative ≤ | Cumulative ≥ | Distribution |
|---|
What Does This Tool Do?
The Dice Combination Sheet takes standard dice notation — like 3d6 (roll three
six-sided dice and sum them) — and computes every possible outcome. For each total, it shows
how many dice combinations produce that result, the exact probability as a percentage, and
cumulative probabilities in both directions (chance of rolling at most or at least that value).
A bar chart visualizes the full distribution so you can see the bell curve or flat spread at a glance.
This is useful for game designers balancing mechanics, tabletop RPG players comparing weapon damage dice, probability students studying distributions, or anyone who wants to understand what happens when you roll dice.
Supported Notation
| Notation | Meaning | Example |
|---|---|---|
NdS | Roll N dice with S sides | 3d6 — three six-sided dice |
NdS+M | Roll and add a flat modifier | 1d20+5 — one d20 plus 5 |
NdS-M | Roll and subtract a modifier | 2d6-1 — two d6 minus 1 |
dS | Shorthand for 1 die | d20 — one twenty-sided die |
Features
Full Probability Table
Every possible sum with its exact combination count, percentage probability, and cumulative odds in both directions.
Distribution Chart
A bar chart drawn on canvas showing the probability distribution. See the classic bell curve for multi-die rolls or the flat line for a single die.
Quick Stats
At-a-glance stats: minimum, maximum, mean (expected value), and standard deviation for the roll.
Flexible Notation
Supports NdS, NdS+M, NdS-M, and shorthand like d20. Presets for the most common rolls are one click away.
Export Options
Copy the full table as CSV to your clipboard, download it as a CSV file, or save the distribution chart as a PNG image.
Instant Calculation
Results compute immediately using dynamic programming — no simulation or sampling. Every probability is exact.
How to Use
- Enter dice notation in the input field using the format
NdS(e.g.,3d6), optionally with a modifier like+5or-2. Or click a preset chip to fill it in automatically. - Click Generate (or press Enter) to compute the distribution. The tool parses your input, calculates every combination, and displays the results.
- Review the stats — minimum, maximum, mean, and standard deviation appear at the top.
- Read the chart — the bar chart shows the probability of each possible sum. Taller bars mean more likely outcomes.
- Explore the table — every row shows one possible sum, the number of ways to roll it, the probability, and cumulative odds. The visual bar on the right gives a quick sense of relative likelihood.
- Export your results — copy as CSV, download the CSV file, or save the chart as a PNG image.
Example
Entering 3d6 generates the probability table for rolling three standard six-sided dice.
The minimum sum is 3 and maximum is 18, with 216 total combinations. The most probable outcome is
10 or 11, each occurring in about 12.5% of rolls. The distribution forms a symmetric bell curve
centered on 10.5 (the mean). The cumulative columns tell you, for example, that you have roughly
a 37.5% chance of rolling 9 or less, and a 62.5% chance of rolling 10 or more.
Frequently Asked Questions
How does it calculate the probabilities?
The tool uses dynamic programming (convolution) to compute exact combination counts. It starts with one die and iteratively adds each additional die, tracking how many ways each sum can be reached. No random sampling is involved — every value is mathematically exact.
What's the largest roll I can compute?
Practical limits depend on your browser, but rolls like 10d10 (10 billion combinations) compute almost instantly. Very large rolls (e.g., 100d6) work but the table will be long. The tool handles any input where the total number of outcomes fits in JavaScript's number precision.
What do the cumulative columns mean?
"Cumulative ≤" shows the probability of rolling that value or lower. "Cumulative ≥" shows the probability of rolling that value or higher. For example, on 1d20 the row for 15 shows Cumulative ≥ 30%, meaning you have a 30% chance of rolling 15 or higher.
Can I use custom die sizes like d3 or d100?
Yes. Any positive integer works as the die size — d3, d7, d100, d37, whatever you need. The notation is the same: 2d3, 1d100+10, etc.
What about modifiers?
Add +N or -N after the dice to apply a flat modifier. For example, 1d20+5 shifts the entire distribution up by 5 (range becomes 6–25). The modifier is applied to the sum, not to each die individually.
Are the probabilities exact?
Yes. The tool computes every combination, not a Monte Carlo estimate. The percentages shown are exact to the precision displayed. Very large combination counts may show slight rounding in the percentage column but the combination counts themselves are exact.