RandoziDice Sum Distribution Calculator
Pick the number of dice, their sides and a modifier. The page counts exactly how many ways each total can come up out of all outcomes, shows the fraction and the percentage for each, draws a histogram, gives the chance of reaching a target and copies the whole table as CSV.
Chance of 10 or more
16.6667 %
2d6 · 11 possible totals from 2 to 12 · 36 equally likely outcomes · average 7
| Total | Ways | Fraction | % |
|---|---|---|---|
| 2 | 1 | 1/36 | 2.7778 |
| 3 | 2 | 2/36 | 5.5556 |
| 4 | 3 | 3/36 | 8.3333 |
| 5 | 4 | 4/36 | 11.1111 |
| 6 | 5 | 5/36 | 13.8889 |
| 7 | 6 | 6/36 | 16.6667 |
| 8 | 5 | 5/36 | 13.8889 |
| 9 | 4 | 4/36 | 11.1111 |
| 10 | 3 | 3/36 | 8.3333 |
| 11 | 2 | 2/36 | 5.5556 |
| 12 | 1 | 1/36 | 2.7778 |
Ways = number of outcomes giving that total; fraction = ways out of all outcomes (sides to the power of dice).
Exact counts for play and study. The page gives no help with betting, and nothing you type leaves your browser.
How it works
- Enter the number of dice (1 to 20) and the number of sides (2 to 100).
- Add a modifier if you need one, and a target total if you want its chance.
- Read the counts, fractions and percentages in the table, and the histogram.
- Copy the summary, or the full table as CSV for a spreadsheet.
What people use it for
Exact odds, not rounded
See that 7 on 2d6 is exactly 6 ways out of 36, and keep the fraction.
A spreadsheet of a dice pool
Copy the CSV of 5d8 and chart it or reuse the counts.
Teaching combinations
Show students how the counts for 2d2 (1, 2, 1) grow into the bell shape of many dice.
Questions
- How is the distribution computed?
- By adding one die at a time. The number of ways to reach a total with k dice is the sum of the ways to reach the previous 1 to S totals with k − 1 dice (a convolution). All counts are exact whole numbers, so every fraction is count ÷ S^N. The chance of reaching a target adds the counts of all totals at or above it.
- What are the limits?
- Up to 20 dice, 100 sides and a modifier of ±10 000, which gives at most 1 981 different totals. The table shows the first 100 totals; the copied CSV has all of them. Large counts are shown with all their digits and wrap on small screens.
- What is in the CSV?
- One header line then one line per total, with the columns sum, count, total and probability, separated by commas and ending lines with CRLF as RFC 4180 asks. Every cell is a plain number, so a spreadsheet will not read any of them as a formula. The probability is rounded to 10 decimals, or written in scientific notation below 1e-6.
- How does it differ from the dice probability calculator?
- This page keeps the exact fractions and counts, draws the histogram and exports the whole table as CSV. The odds are for play and study; the page gives no help for betting.