Dice Probability Calculator
Calculate the probability of rolling any sum with dice — 2d6, 3d6 and more. See exact, at-least and at-most probabilities.
P(sum = 7)
16.67%
6 of 36 outcomes
P(sum ≥ 7)
58.33%
P(sum ≤ 7)
58.33%
All dice are fair and independent. Sums below the number of dice or above sides × dice are impossible.
Dice Probability Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Calculate the probability of rolling any sum with dice — 2d6, 3d6 and more. See exact, at-least and at-most probabilities. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: dice probability calculator · dice roll probability · 2d6 probability
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard statistical formulas as defined in textbooks and statistical software. All calculations are performed instantly in your browser using JavaScript — no data is sent to any server.
Formulas follow the conventions used in academic statistics, including population and sample variants where they differ.
When to Use This Calculator
Use the dice probability calculator whenever a game, exam problem or simulation needs probabilities of dice sums — the staple of board games like Ludo and Monopoly, dice-based betting games, and probability chapters in Indian school and JEE syllabi. The calculator handles any number of dice and any number of sides, so it also covers tabletop d20 systems and custom dice for game designers. Teachers use it to set and check homework problems, while game developers sanity-check the odds their rules create. Beyond games, the same discrete-sum mathematics applies to problems like rolling totals in statistical simulations. The exact, at-least and at-most probabilities together answer every phrasing a problem or player can throw at you, and the way count makes the arithmetic visible so results can be verified by hand.
How to Use This Calculator
- Step 1: Enter the number of dice being rolled, such as 2.
- Step 2: Enter the number of sides per die — 6 for standard dice, or any other value.
- Step 3: Enter the target sum you want the probability for, such as 7.
- Step 4: Read the exact probability, the number of ways, and the at-least and at-most probabilities.
Worked Example
Two friends in Jaipur settle a dispute with a roll of two dice, and one needs a sum of at least 10 to win. Enter 2 dice, 6 sides and target 10: the probability of exactly 10 is 3/36, but the calculator's at-least figure — summing 10, 11 and 12 — is 6/36, or 16.67%. For the most common sum, 7, there are 6 ways out of 36, also 16.67%. Rolling three dice for a sum of 10 gives 27 ways out of 216, exactly 12.5%, the calculator's most likely three-die sum.
Tips and Common Mistakes
- •Tip 1: Use the at-least and at-most cards for 'rolling 8 or more' style questions, which are more common than exact sums.
- •Tip 2: Sums below the number of dice or above sides × dice have probability zero — the calculator handles these bounds.
- •Tip 3: For repeated single-face outcomes like 'three sixes in five rolls', switch to the binomial distribution calculator.
- ✗Mistake 1: Treating each sum as equally likely — a sum of 7 is six times more likely than 2 or 12 on two dice.
- ✗Mistake 2: Entering huge dice counts with many sides — the outcome space overflows, and the calculator politely refuses.
Frequently Asked Questions
How do I calculate the probability of a dice sum?
The calculator counts the number of ways a sum can occur and divides by the total outcomes (sides raised to the number of dice). For two six-sided dice, a sum of 7 has 6 ways out of 36, giving a probability of 1/6, or about 16.67% — the most likely sum. Sums of 2 and 12 each have only 1 way.
Why is 7 the most likely sum on two dice?
Because there are more combinations that add to 7: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1. The count rises toward the middle sums and falls toward the edges, so the probability curve for dice sums is triangular rather than flat. This is why 7 dominates games like craps.
What is the probability of rolling at least a certain sum?
The at-least probability adds the ways for every sum from your target up to the maximum. On two six-sided dice, rolling at least 10 has 6 ways (4+6, 5+5, 5+6, 6+4, 6+5, 6+6) out of 36, so the probability is 1/6. The at-most probability is the mirror image, adding sums up to your target.
Does this work for board games like Ludo or Monopoly?
Yes — both use a standard six-sided die, and this calculator covers any number of dice from one up. For games with special rules like double-six rolls in Ludo, use the binomial distribution calculator instead, treating a double-six as a success with probability 1/36 per roll.
Can I use non-six-sided dice?
Yes — the sides field accepts any number of sides from 2 (a coin) upward, so you can model d4, d8, d12 and d20 dice from tabletop role-playing games. The same mathematics applies: total outcomes are sides raised to the number of dice, and the calculator finds the ways for any target sum.
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