Dice Roller

What this calculator does

Roll virtual dice right here, for board games, role-playing games, class lessons, or whenever the real dice have gone missing. Choose how many dice and how many sides, then press Roll. You'll see every die, the total, and how that total compares with a typical roll.

Dice are named by their sides: a d6 has 6 sides and a d20 has 20. You can roll the usual gaming set (d4, d6, d8, d10, d12, d20 and d100), or custom dice with up to 1,000 sides. You can add a modifier, a fixed number like +3. You can also drop the lowest or highest die. That covers rolling 4d6 (four six-sided dice) and dropping the lowest for an ability score. It also covers rolling with advantage or disadvantage on 2d20.

Where it's used

Why this math matters outside the classroom:

• Board games. Players rolling two dice know a total of 7 comes up in 6 of the 36 outcomes, a probability of 1/6.
• Role-playing games. A player who needs 15 or more on a d20 has 6 winning faces out of 20, a 30% chance.
• Classroom probability. Students list all 36 outcomes for two dice and find that totals of 2 and 12 each have a 1/36 chance.
• Taking turns. Six players roll a d6 to choose who starts, giving each player an equal 1/6 chance.
• Average totals. A player rolling three six-sided dice averages 3 × 3.5 = 10.5 per roll over many rolls.

Grade level and standards: Grade 7; Common Core State Standards for Mathematics 7.SP.C.8, 7.SP.C.7.a. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

1. Enter how many dice you want and choose the type of die. Pick Custom to set any number of sides from 2 to 1,000.
2. Choose how to total them: add every die, drop the lowest, or drop the highest.
3. Add a modifier if your game calls for one. Negative modifiers are fine.
4. Press Roll the dice. Every press is a fresh roll that doesn't depend on the last one. Your last ten totals are listed below the button.

What the inputs mean

Number of dice

From 1 to 100 dice. To drop a die, you need at least 2.

Sides per die

Use 2 for a coin-style 1-or-2 roll, or any size up to 1,000.

How to total the dice

Rolling 4d6 and dropping the lowest gives the classic ability-score roll. On 2d20, dropping the lowest keeps the higher die (advantage). Dropping the highest keeps the lower one (disadvantage).

Modifier (added to the total)

A fixed number added to the total after any die is dropped. For example, +5 for a skill bonus or −1 for a penalty.

Formula and method

each die = a whole number from 1 to s, each with probability 1/s
total = sum of the kept dice + modifier
average total (all dice kept) = n × (s + 1) ÷ 2 + modifier
E[lowest of n dice] = Σ (k = 1 to s) ((s − k + 1) ÷ s)^n
E[highest of n dice] = Σ (k = 1 to s) (1 − ((k − 1) ÷ s)^n)
P(total = t) is found by combining the dice one at a time (a convolution)

In the formulas, n is the number of dice, s is the number of sides on each die, and k counts through the faces from 1 to s. E[…] means "the average you'd expect" and P(…) means "the chance of". Σ means "add up" the values for every k.

One fair die with s sides averages (s + 1) ÷ 2. So a d6 averages 3.5 and a d20 averages 10.5. Averages add up, so n dice average n times that. Dropping a die takes away its average. The two longer formulas give the average lowest and highest die. They add up the chance that the lowest (or highest) die reaches each face value.

The chance of each exact total is built one die at a time, a method called convolution. You start knowing the total is 0. Each new die spreads every running total evenly over the next s values. That gives the exact chance of every possible total. From it, the calculator reads the chance of your roll, and of anything higher.

Worked example

Roll 4d6 and drop the lowest to make a character's ability score. The dice land 5, 2, 6 and 3.

1. Drop the lowest die, the 2, and keep 5, 6 and 3.
2. Add the dice you kept: 5 + 6 + 3 = 14.
3. There's no modifier, so the ability score is 14.
4. For comparison, 4d6 drop lowest averages 15,869 ÷ 1,296 ≈ 12.24. So 14 is a little above average.

Result: An ability score of 14. That's about 1.8 above the long-run average of 12.24 for this method.

Understanding the result

The average total is what you'd get on average over many rolls. Any single roll can land anywhere in the possible range. When you add several dice, totals near the middle come up most often. That's why 7 is the most likely total on 2d6, with a 1 in 6 chance.

The chance of your total or more tells you how lucky a roll was. A 5% figure means only about one roll in twenty does as well.

Assumptions and limitations

• Every die is fair. Each face is equally likely, and the dice don't affect each other.
• A d10 is numbered 1 to 10, and a d100 is numbered 1 to 100, rather than 0 to 9 or 00 to 99.
• Each roll starts from a random seed (a starting number) from your browser's crypto.getRandomValues. That seed feeds a well-tested random number generator.
• Exact chances are only shown when all the dice are added up and the number of dice times the sides is 20,000 or less. The roll itself works for any size.
• It rolls one group of matching dice at a time. For mixed groups such as 1d8 + 2d6, roll each group and add the totals.
• Exploding dice, rerolls and counting successes aren't supported.

Frequently asked questions

How this calculator is checked

Method: Uniform discrete dice; exact total distribution by convolution; expected minimum and maximum of n dice from tail-sum formulas; xoshiro128** seeded from crypto.getRandomValues. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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