Dice Roller
Roll any dice in standard notation, from a single d6 to 1d20+5 or 4d6 keep-highest-3, and see each die, the total and the exact chance of every total, so you know how lucky the roll was.
How to Use
- Type dice in standard notation: 1d6, 2d6+3, 1d20+5, 3d8−2, d% for d100. Add groups with +, such as 1d20+1d4+2.
- Keep the highest or lowest dice with kh or kl: 4d6kh3 drops the lowest of four, 2d20kh1 is advantage, 2d20kl1 disadvantage.
- Press Roll; dropped dice are shown faded.
- Read the total, the chance of rolling that or higher, the average and the possible range.
- The bar chart gives the exact chance of every total, with your roll highlighted.
Worked Example
An attack roll: 1d20+5 against armour 15. You need 10 or more on the d20, which is 11 faces of 20: 55%. With advantage (2d20kh1+5) you miss only if both dice show 9 or less: 1 − (9/20)² = 79.75%.
Three dice. 3d6 has 6³ = 216 outcomes. A total of 15 or more needs one of 20 combinations (10 + 6 + 3 + 1 for 15, 16, 17, 18), so 9.26%; 10 and 11 are the most common totals, 27 ways each (12.5%).
The common mistake: assuming totals are equally likely. With 2d6, a total of 2 needs both dice to show 1, a 1 in 36 chance, while 7 can be made six ways (1 in 6).
Show Work
Dice Maths
Five Thousand Years of Dice
The oldest known dice come from the Middle East around 3000 BC, and the Royal Game of Ur used four-sided pyramid dice. Roman soldiers played with cubic dice almost identical to modern ones, with opposite faces adding to 7. Gerolamo Cardano’s Liber de ludo aleae (written around 1564) was the first study of dice probabilities.
The d4, d8, d12 and d20 of role-playing games became popular with Dungeons & Dragons in 1974; the NdS notation, now standard, comes from those rulebooks.
About This Tool
This dice roller reads standard dice notation with modifiers, several groups and keep-highest or keep-lowest, rolls fairly with your browser’s cryptographic random source, and shows every die. Unlike most rollers it also works out the exact probability of every possible total, so you can see how likely your roll was.
Everything runs in your browser; nothing is sent anywhere.
Related tools: Coin Flip, Probability Calculator, and Convolution Calculator.
Frequently Asked Questions
What does 2d6+3 mean?
Roll two six-sided dice, add them, then add 3. The first number is how many dice, the number after d is how many sides, and the + or − is a fixed modifier. 2d6+3 ranges from 5 to 15 with an average of 10.
Why is 7 the most common total with two dice?
Because more combinations make it: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1, six of the 36 equally likely pairs (16.7%), while 2 and 12 each have only one way (2.8%). Adding dice makes middle totals more common; with more dice the shape approaches a bell curve.
What do advantage and keep highest mean?
Roll more dice than you need and keep the best. Advantage in Dungeons & Dragons is 2d20kh1, roll two d20s and keep the higher, which raises the average from 10.5 to 13.8 and the chance of 15 or more from 30% to 51%. 4d6kh3, the classic way to roll ability scores, averages 12.24 instead of 10.5.
Are these rolls fair?
Yes. Each die uses your browser’s cryptographic random source with rejection sampling, so every face is exactly equally likely, which is better than many physical dice: cheap dice with drilled pips and rounded corners can favour some faces by a few percent.
How are the probabilities worked out?
Exactly, by combining the dice one at a time (a convolution) and counting every way to reach each total. For keep-highest rolls, every possible combination of the dice is checked; only for very large keep rolls is the chart estimated by simulation, and the page says so.
How do I use the Dice Roller?
Simply pick your options and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Board games
2d6 for Monopoly or Catan: 7 comes up 1 time in 6.
Role-playing
1d20+5 attack: 15 or more hits 55% of the time.
Character creation
4d6 drop the lowest, six times, for ability scores.
Damage rolls
8d6 fireball: 8 to 48, average 28.
Teaching
See how sums of dice approach a bell curve as dice are added.
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