Dice Roller

About the Dice Roller

Dice are one of the oldest ways of generating chance, used in board games for thousands of years and in modern tabletop role-playing games with dice of every shape. But dice go missing, roll off tables, and are not always to hand. A virtual dice roller gives a fair roll instantly — and, unlike physical dice, it can also tell you how likely your result was.

This dice roller rolls any number of dice with 4, 6, 8, 10, 12, 20 or 100 sides, plus a modifier, using the standard notation such as 2d6 or 3d6+2. It shows each die, the total, the average and range for that roll, the chance of the exact total and of rolling it or higher, and the most likely total.

How to Use the Dice Roller

Enter the number of dice.

Choose the number of sides: d4, d6, d8, d10, d12, d20 or d100.

Enter any modifier to add or subtract from the total.

Press Calculate to roll, and again to roll again. Enter a seed if you need to repeat the same rolls.

How the Odds Are Worked Out

  average        =  dice × (sides + 1) ÷ 2 + modifier
  range          =  dice + modifier  to  dice × sides + modifier
  outcomes       =  sides ^ dice   equally likely combinations
  chance of a total  =  combinations giving that total ÷ all combinations

The calculator builds the exact distribution of totals by combining one die at a time, so the probabilities are exact, not simulated.

Step-by-Step Example

2d6 — two six-sided dice.

  Average:      2 × (6 + 1) ÷ 2         =  7
  Range:        2 to 12
  Outcomes:     6 × 6                   =  36
  Chance of 7:  6 ÷ 36                  =  16.7%
  8 or more:    15 ÷ 36                 =  41.7%

3d6+2.

  Average:      3 × 3.5 + 2             =  12.5
  Range:        5 to 20

Dice Notation

Tabletop games write dice as NdS: N dice with S sides. 1d20 is one twenty-sided die, 4d6 is four six-sided dice added together, and a modifier is added at the end: 2d8+3 means roll two eight-sided dice and add three. d100, or percentile dice, gives a number from 1 to 100, often rolled as two ten-sided dice for tens and units.

Why Some Totals Are More Likely

With a single die, every face is equally likely. With two or more dice, middle totals become much more common because there are more ways to make them. Two d6 can make 7 in six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), but 2 and 12 in only one way each. The more dice you add, the more the totals cluster around the average, forming the familiar bell shape. That is why games use 2d6 for predictable results and a single d20 when every outcome should be equally likely.

Common Probabilities

Fairness of Virtual Dice

Real dice can be slightly unbalanced by manufacturing flaws, rounded edges or the way they are thrown. The virtual dice here use your browser's cryptographic random generator, so each face has exactly the same chance on every roll. Rolls are independent: a string of low rolls does not make a high roll more likely next time.

Dice in Games

Different games use dice for different effects. Board games such as backgammon and many family games use pairs of six-sided dice, where 7 is common and doubles add excitement. Role-playing games use a d20 for most checks, so every result from 1 to 20 is equally likely and a "natural 20" is a memorable 5 percent event, while damage is often rolled with several smaller dice for a more predictable result. Some games use "advantage": roll two d20s and keep the higher, which raises the average from 10.5 to about 13.8 and makes a 20 nearly twice as likely.

Teaching Probability With Dice

Dice are ideal for teaching probability because every outcome is easy to see. Listing all 36 outcomes of two dice in a grid makes it clear why 7 is the most common total. Rolling many times and recording the results shows how the observed frequencies settle towards the calculated probabilities — a practical demonstration of the law of large numbers. With the calculator, students can compare their rolls with the exact odds after every throw.

Percentile Dice

A d100, or percentile roll, gives every number from 1 to 100 an equal 1 percent chance. Games use it for rare events and percentage checks: a 15 percent chance succeeds on a roll of 15 or less. With two physical ten-sided dice, one is read as tens and the other as units, and 00 with 0 counts as 100.

Understanding Your Result

Total is the sum of the dice plus the modifier.

Rolls shows each die and how the total was made.

Average and range gives the average and the lowest and highest possible totals.

Odds of this roll gives the chance of this exact total and of this total or more.

Most likely total shows the most common total and its chance.

Worth knowing explains independent rolls and seeds.

When Should You Use This Calculator?

Playing board games without dice to hand.

Tabletop role-playing games with many dice.

Teaching probability in the classroom.

Checking the odds of a roll before deciding a move.

Making random decisions.

Common Mistakes

Thinking a total is "due" after it has not come up.

Treating all totals on 2d6 as equally likely.

Forgetting the modifier in the range.

Confusing d100 with two separate d10 totals.

Using a seed when you want a fresh roll.