Dice Roller & Probability Calculator

The expected value of a single N-sided die is calculated as (N + 1) / 2. For example, a D6 has an average of (6 + 1) / 2 = 3.5. For multiple dice with a modifier, multiply the single die average by the number of dice and add the modifier. For 2D6 + 5, the expected average is (2 × 3.5) + 5 = 12.

There are 36 possible outcomes when rolling two six-sided dice. The sum of 7 is the most likely outcome with 6 combinations (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), giving a probability of 6 / 36 or 16.67%. The sums of 2 and 12 are the least likely, each having only 1 combination (1/36 or 2.78%).

As you roll more dice, the probability distribution of the sum transitions from a flat profile (for 1 die) to a bell curve (normal distribution). This means the sum is highly likely to fall near the middle average, and extreme results (like rolling all 1s or all maximums) become exponentially rarer.

These designations represent the number of sides on a die, commonly used in tabletop roleplaying games like Dungeons & Dragons. A D4 is a tetrahedron (4 sides), D6 is a cube (6 sides), D8 is an octahedron (8 sides), D10 is a pentagonal trapezohedron (10 sides), D12 is a dodecahedron (12 sides), and D20 is an icosahedron (20 sides).

A D100 roll (often called a percentile roll) is typically done using two 10-sided dice. One die represents the tens digit (00, 10, 20... 90) and the other represents the units digit (0-9). A roll of '00' and '0' is read as 100.