Dice Roller

Reading Dice Notation

NdS means roll N dice with S sides and add them: 3d6 is three six-sided dice, 1d20 one twenty-sided die. A modifier adds or subtracts a fixed number, so 1d20+5 ranges from 6 to 25. Enter a target to get the chance of rolling that total or higher, the usual question in tabletop games. One die is equally likely to land on any face; adding dice piles the probability toward the middle.

How the Exact Odds Are Calculated

The calculator builds the full distribution one die at a time, counting how many of the S^N equally likely outcomes produce each total. The average is N × (S + 1) ÷ 2 plus the modifier, and the standard deviation is √(N × (S² − 1) ÷ 12). For 2d6 that is 2 × 7 ÷ 2 = 7 and √(2 × 35 ÷ 12) = 2.415. Six of the 36 outcomes (1+6, 2+5, 3+4 and their reverses) total 7, so 7 has a 1/6 chance.

Odds for Two Six-Sided Dice

Common Rolls Compared

A single d20 is a flat 5% per face, so a +5 modifier adds exactly 25 points to the chance of any target in range. Adding dice narrows the spread relative to the range: 3d6 and 1d20 cover similar ranges, but 3d6 lands near its middle far more often.

Common Mistakes With Dice Odds

Adding probabilities across rolls. The chance of at least one 6 in two rolls is 11/36, not 2/6, because both dice can show 6 at once.

Expecting a total to be “due.” Each roll is independent; a long run without a 7 does not make the next 7 more likely.

Using it for rules it does not model. The calculator sums all dice. Rolling 4d6 and dropping the lowest, rerolling ones, or rolling with advantage each change the distribution.

Frequently Asked Questions

How to Use This Calculator

1. Enter dice notation — like 2d6, 4d6 or 1d20+5.
2. Set a target — to see the chance of reaching it.
3. Roll and analyze — for odds and a random roll.
4. Read the distribution — range, average, most and least likely totals.