The dice probability calculator computes exact odds for any dice combination. Enter standard notation like 3d6+2, advantage as 2d20kh1, or the ability score roll 4d6kh3 to see probability distributions, expected value, and hit chances for your target number.
Dice Notation
NdX — roll N dice with X sides+/-N — add/subtract modifierNdXkhM — keep highest M diceNdXklM — keep lowest M diceProbability Distribution
Enter dice notation and click Calculate to see probabilities
How to Use the Dice Probability Calculator
Whether you are a D&D Dungeon Master balancing spell damage or a board game designer testing your mechanics, the dice probability calculator gives you exact probabilities — not estimates — for any combination of dice and modifiers.
Step 1: Enter Dice Notation
Type your dice expression in standard notation. 2d6 means roll two six-sided dice. 3d8+4 means roll three eight-sided dice and add 4. Use presets like "Advantage" or "4d6kh3" for common D&D rolls.
Step 2: Set a Target Number
Enter the number you are trying to hit. Choose ≥ (at least) for most rolls where higher is better — like needing a 15 or higher on a saving throw. Choose ≤ for rolls where lower is better. Choose = for exact matches, useful when asking "what are the odds of rolling exactly 7 on 2d6?"
Step 3: Read the Distribution Chart
The bar chart shows the probability of every possible result. For 2d6, the distribution is a triangle (7 is the most common). For a single d20, it is flat (every value equally likely). Rolls using the keep-highest mechanic (advantage) skew toward high numbers, creating a right-skewed distribution.
Common Dice Probability Examples
Hitting AC 15 with a +5 attack bonus on a d20 requires rolling 10 or higher — a 55% chance. With advantage, that climbs to about 80%. Fireball deals 8d6 damage averaging 28 but varies from 8 to 48. The 4d6kh3 ability score roll averages 12.24 and can produce values from 3 to 18. Use this calculator to understand those mechanics before your next session.
FAQ
Is this dice probability calculator free?
Yes, completely free with no signup or account required. All calculations happen in your browser — enter your dice notation and get instant results.
Is my data sent to any server?
No. Everything runs locally in your browser using JavaScript. Nothing is transmitted to any server at any time.
What dice notation does this calculator support?
Standard notation like 2d6, 3d8+4, and 1d20-2. It also supports advantage (2d20kh1), disadvantage (2d20kl1), and the D&D ability score roll (4d6kh3 — roll 4 dice, keep the highest 3). The 'k' modifier means 'keep' and 'h'/'l' means highest or lowest.
What does 'advantage' mean in dice terms?
Advantage in D&D 5e means rolling two d20s and taking the higher result. In dice notation this is 2d20kh1 — roll 2 d20s, keep the highest 1. This significantly increases your probability of rolling high: the chance of rolling 15 or higher goes from 30% with one d20 to around 51% with advantage.
How is the probability distribution calculated?
The calculator uses exact combinatorics for standard rolls (not simulation). It enumerates all possible outcomes for the dice combination, applies modifiers, and calculates the exact probability of each result. This gives precise percentages rather than approximations.
What is expected value for a dice roll?
Expected value is the average result you would get if you rolled the dice infinitely many times. For a single d6, the expected value is 3.5. For 2d6, it's 7. For 2d20kh1 (advantage), the expected value is about 13.8, compared to 10.5 for a single d20.
What does standard deviation mean for dice rolls?
Standard deviation measures how spread out the results are around the average. A low standard deviation means results cluster tightly around the expected value. Rolling many dice and summing them produces a bell-curve distribution with low standard deviation — for example, 10d6 is almost always between 20 and 50, while 1d60 is uniformly spread.
Can I calculate 4d6 drop lowest for ability score rolls?
Yes. Enter '4d6kh3' — this means roll 4 six-sided dice and keep the highest 3. The calculator shows the full probability distribution and expected value, which is approximately 12.24 per roll — higher than a standard 3d6 average of 10.5.