Dice Roller

Roll Virtual Dice

Dice Roller Formula

Formula

\[ \begin{aligned} T&=\sum_{i=1}^{n}r_i+M,\\ T_{\min}&=n+M,\\ T_{\max}&=\sum_{i=1}^{n}s_i+M,\\ \operatorname{E}(T)&=\sum_{i=1}^{n}\frac{s_i+1}{2}+M. \end{aligned} \]

Where:

\(T\) — total with modifier
\(n\) — number of dice
\(r_i\) — result of die \(i\)
\(s_i\) — number of sides on die \(i\)
\(M\) — modifier added to the dice

For a normal roll, the total is the sum of the dice faces plus the modifier. The minimum, maximum, and average describe possible totals across many rolls—not a prediction of the next roll. A single d20 rolled with advantage or disadvantage uses the higher or lower of two throws instead.

Dice Roller – Calculation Example

Example: With the default settings of two d6 dice and a modifier of 0, suppose the dice show 3 and 5.

\[ T=3+5+0=8 \]

\[ T_{\min}=2,\qquad T_{\max}=12,\qquad \operatorname{E}(T)=7 \]

Result: this roll totals 8. Its possible totals run from 2 to 12, with an average of 7. Your dice faces—and therefore your total—will usually differ.

How to use the Dice Roller

Enter a whole number from 1 to 20 in Number of dice. The default is 2.
Choose a Die type: d4, d6, d8, d10, d12, d20, or d100. To use another size, select Custom sides and enter a whole number from 2 to 1,000 in Custom sides.
Enter a positive, negative, or zero whole number in Modifier. It is added once to the sum, not once per die.
Alternatively, enter an expression in Dice notation (optional), such as 3d6+2 or 1d20 + 1d4. Notation overrides Number of dice, Die type, Custom sides, and Modifier.
Choose d20 roll mode. Leave it at Normal for an ordinary roll, or select advantage or disadvantage when the roll consists of exactly one d20.
Read Dice faces and Total with modifier. To repeat the same setup without changing its values, switch Toggle to roll again. Changing a setting also produces a new roll.

What the roll results mean

A die labeled d6 has six numbered faces, from 1 through 6; a d20 has faces from 1 through 20. The Dice Roller generates a face for each die and adds those results together. Total with modifier is the value to use if your game or activity calls for a single number. Dice faces shows the individual outcomes; d6 results appear as pip symbols, while other die types show numbers.

Minimum possible total assumes every die shows 1, while Maximum possible total assumes every die shows its highest face. The modifier shifts both endpoints. A negative modifier can make the minimum total zero or negative even though every die face is positive. These endpoints describe what is possible, not what is likely: with the default 2d6 setup, a total of 2 occurs only when both dice show 1.

Average possible total is the expected value over many rolls. For two d6 dice with no modifier, it is 7, but a particular roll can produce any integer from 2 to 12. Totals in the middle are more common because more face combinations produce them: six of the 36 equally likely combinations total 7, while only one totals 2. The displayed average is not a running average of your recent results.

With Advantage: keep highest, the calculator throws two d20s and uses the higher face. With Disadvantage: keep lowest, it uses the lower face. Both faces are shown and marked kept or dropped; even a tie contributes just one face to the total. Before any modifier, the possible range remains 1–20, but the average changes from 10.5 for a normal d20 to 13.825 with advantage or 7.175 with disadvantage.

Notation, limits, and practical tips

Dice notation is useful when a roll mixes die sizes. For example, 1d20+1d4-2 rolls one d20 and one d4, then subtracts 2 from their sum. You can omit the count for a single die, as in d20. Spaces are allowed. Dice terms must be added rather than subtracted; the notation field accepts whole-number modifiers but not multiplication or fractions.

A roll can contain at most 20 dice, each with 2–1,000 sides. A standard Modifier must be between −1,000,000 and 1,000,000; the combined modifier in dice notation has the same limits. Advantage and disadvantage work only for a single d20, whether selected through the fields or entered as 1d20. They cannot be applied to a mixed roll such as 1d20+1d4.

Last 10 rolls records recent valid rolls on the current page, showing the dice setup, thrown faces, and total. Toggling the repeat checkbox makes another roll with the same settings; merely reading the results does not. The roller uses the browser’s cryptographic random-number generator and avoids modulo bias when mapping random values to die faces. Results are suitable for games and informal decisions, but past rolls do not make any particular face more likely on the next roll.

If a group uses a die to choose who goes first or assign a task, agree on what each outcome means before rolling. For shared expenses, use the Bill Split calculator to work out amounts rather than relying on a random result. If the activity is part of a trip, the Travel Budget calculator can help plan the costs separately.

Frequently Asked Questions

How do I calculate the chance of a particular dice total by hand?

Count the combinations that produce the total, then divide by the number of equally likely combinations. For 2d6, there are \(6\times6=36\) combinations. A total of 9 has four: 3+6, 4+5, 5+4, and 6+3. Its probability is therefore \(4/36=1/9\), or about 11.1%. Count the two dice separately even when their faces are reversed.

What is the chance of rolling at least one six on 3d6?

Calculate the opposite outcome first: no die shows a six. Each d6 has a \(5/6\) chance of avoiding six, so the chance that all three do is \((5/6)^3=125/216\). Subtract from one to get \(91/216\), or about 42.1%, for at least one six. This method works for other “at least one” questions when the rolls are independent.

How does a d100 roll relate to percentile dice?

A d100 result is a whole number from 1 to 100, with each value equally likely. Physical percentile dice often use two ten-sided dice to represent tens and ones; under a common convention, 00 and 0 together mean 100. Check your game’s convention before comparing a virtual d100 result with physical dice, especially for outcomes involving 0 or 100.

How likely is a natural 20 with advantage or disadvantage?

With advantage, either d20 can produce the kept 20, giving a probability of \(1-(19/20)^2=9.75\%\). With disadvantage, both dice must show 20 for the kept result to be 20, giving \((1/20)^2=0.25\%\). A normal d20 has a 5% chance. Whether that result counts as a critical success depends on your game’s rules and the type of roll.

Can I roll 4d6 and drop the lowest die?

You can roll 4d6 and inspect the four faces, but the displayed total includes all four dice. To use a “drop the lowest” rule, subtract the smallest face yourself; do not enter it as a negative dice term, because the notation field does not support dropping dice. On a tie for lowest, drop only the number of dice your rule specifies.

How do I find the chance that a d20 roll meets a target number?

For a normal d20 roll with modifier \(M\) and target \(D\), count the faces satisfying \(r+M\ge D\), then divide by 20. For example, a +3 modifier against a target of 15 succeeds on faces 12–20: 9 faces, or 45%. If the target is outside the reachable range, the chance is 0% or 100%. Some games add special rules for natural 1s and 20s.