Dice Rolling Guide | The Dice Roller

Dice notation

1d6 means one six-sided die. 2d6 means two, usually summed. A +3 modifier adds three to the total. On this site the modifier is applied once per action.

Expected values

One fair s-sided die averages (s + 1) / 2 over repeated rolls. A D6 averages 3.5 and a D20 averages 10.5. That is the average a fair dice roller approaches over many rolls; these are long-run expectations, not guaranteed results.

Range and average of one fair die
Die	Range	Average
D4	1 to 4	2.5
D6	1 to 6	3.5
D8	1 to 8	4.5
D10	1 to 10	5.5
D12	1 to 12	6.5
D20	1 to 20	10.5
D100	1 to 100	50.5

Multiple dice

For n independent dice with s sides and modifier m, expected total is n(s + 1)/2 + m. The smallest total is n + m and largest is ns + m.

Example: 3d8 + 2 averages 3 × 4.5 + 2 = 15.5, with a range from 5 to 26.

Fairness and random results

A uniform roller assigns equal probability to each face. Repeats and short uneven runs are normal. A small sample alone does not demonstrate that a roller is unfair.

The Dice Roller draws each die from the browser’s cryptographic random number generator and uses rejection sampling, which discards the few raw values that would otherwise favour low faces.

Pick the right tool

Use the homepage dice roller for custom sides and quantities, the two dice roller for a pair of D6s, the D&D dice roller for tabletop presets and the letter dice roller for alphabet selections. The auto dice roller repeats a roll at a steady interval.