Free Dice Probability Calculator
Calculate odds for any dice roll — advantage, disadvantage, pools, and target numbers.
Probability distribution
What is a dice probability calculator?
A dice probability calculator is a free online tool that helps you compute the exact probability of any outcome when rolling one or more dice. It runs entirely in your browser — no signup, no app, and no data is ever sent to a server.
A dice probability calculator computes the odds of any dice roll outcome for tabletop RPGs, board games, and gambling games. Whether you need to know the chance of hitting a DC 15 in D&D 5th edition with advantage, the probability of rolling a specific total in Yahtzee, or the success rate of a dice pool in Vampire: The Masquerade, this tool covers all common roll mechanics. Understanding the actual probabilities helps you make better tactical decisions during play — no more assuming a +2 bonus is the same as advantage.
How it works
For single dice, the calculator uses simple arithmetic: (sides − target + 1) ÷ sides. For multiple dice, it uses generating function convolution to compute exact probability distribution. Advantage and disadvantage use the standard D&D formula: 1 − ((n−1)/20)² for advantage, (21−n/20)² for disadvantage. Dice pools use the binomial distribution: P(k successes) = C(n,k) × p^k × (1−p)^(n−k).
When to use a dice probability calculator
Dungeon Masters balancing encounters and setting DCs. Players choosing between abilities that grant advantage versus flat bonuses. Board game strategists calculating the risk of different moves. Game designers testing dice mechanics and balancing probability curves for their own tabletop RPG or board game systems. Teachers demonstrating binomial distribution concepts.
Common mistakes with dice probability
The most common mistake I see players make is thinking advantage is the same as a flat +5 bonus. In D&D 5th edition, advantage on a d20 gives an effective bonus of about +3.3 on average, but the actual benefit varies significantly by target number. For a DC 10 check, advantage improves your chance from 55% to 79.75% — equivalent to roughly +5. For a DC 18 check, advantage goes from 15% to 27.75% — equivalent to only about +2.5. The calculator shows exact probabilities so you can make informed decisions.
Another common error is misunderstanding how dice pools work. In games like Vampire or Warhammer, rolling more dice doesn't just increase your chance of success — it changes the shape of the probability distribution entirely. With 3 dice at difficulty 7+ (40% success per die), you have a 78.4% chance of at least one success but only a 31.1% chance of two or more. Adding more dice increases the chance of multiple successes more than it increases the chance of at least one. The calculator handles this with exact binomial distribution math.
I also find that many players don't realize the probability of rolling a specific total on multiple dice follows a bell curve, not a flat distribution. The chance of rolling exactly 7 on 2d6 is 16.7%, but the chance of rolling 2 or 12 is only 2.8% each. That 6:1 ratio means you should plan for average outcomes, not extremes. Game designers who make critical failures happen on a 2 on 2d6 are creating an event that only occurs 2.8% of the time — far rarer than most players assume.
How to use this calculator
- Choose your dice type — Select d4, d6, d8, d10, d12, d20, or custom.
- Enter dice count and target — Input how many dice and what target number you need to meet or beat.
- Choose roll modifier — Select normal, advantage, disadvantage, or a dice pool count-success mechanic.
Frequently asked questions
How do I calculate dice roll probability?
Probability = number of ways to succeed ÷ total possible outcomes. For a single d20, each outcome has a 5% chance. For 2d6, there are 36 total outcomes. To roll a 7: there are 6 ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so probability = 6 ÷ 36 = 16.7%. The more dice, the more the distribution clusters toward the average.
What is the probability of rolling a d20 with advantage?
With advantage (roll twice, take higher), the probability of rolling at least a target number n is 1 − ((n−1)/20)². For a DC 15 check: normal = 30%, advantage = 51%, disadvantage = 9%. Advantage adds roughly +3 to +5 effective bonus depending on the target.
How do dice pool probabilities work?
In games like Vampire: The Masquerade or Warhammer, you roll a pool of d10s and count successes (typically 7-10). Expected successes = pool size × success probability. For 8 dice with 50% success chance (7+ on d10): expected = 4 successes. The calculator computes exact probabilities using binomial distribution.
What is the most likely total when rolling multiple dice?
For multiple dice, the most likely total is the average of the range. For 2d6 (range 2-12): average = 7, probability 16.7%. For 3d6 (range 3-18): average = 10.5, with 10 and 11 each having 12.5%. The distribution follows a bell curve that narrows relative to the range as you add more dice.
How do I calculate the probability of rolling at least a certain number?
Count the successful outcomes and divide by total outcomes. For a d20 needing 15 or higher: outcomes 15-20 = 6 successful outcomes out of 20 = 30%. For multiple dice, sum the probabilities of all totals at or above your target. With advantage: P = 1 − ((n−1)/20)². The calculator handles all these cases automatically.
What is the difference between advantage and a +2 bonus?
A +2 bonus shifts every outcome up by 2, which is consistent across all target numbers. Advantage gives diminishing returns the higher the target number. Against DC 10: advantage = 79.75%, +2 bonus = 65%. Against DC 18: advantage = 27.75%, +2 bonus = 45%. Advantage is better for easy checks; flat bonuses are better for hard checks.