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Dice Sum Probability Calculator

Calculate the probability of rolling a specific sum with two or more six-sided dice.

Result

Probability
-%
Ways to Roll This Sum
- of 36

About the Dice Sum Probability

The Dice Sum Probability Calculator finds the exact odds of rolling a specific total with two or more standard six-sided dice. It's aimed at board game and tabletop RPG players who want to know, for instance, how likely a roll of 7 is with two dice compared to a roll of 10 with three dice, without resorting to trial and error at the table.

How It Works

You enter how many dice are being rolled, from 1 to 6, and the target sum you want the odds for. The calculator builds the complete distribution of ways to reach every possible sum by combining the dice one at a time, counts how many of those combinations hit your exact target sum, and divides that by the total number of possible dice-face combinations to get a probability.

Probability = (number of dice-roll combinations that sum to the target) / 6^(number of dice) x 100%. The distribution of ways to reach each sum is built by convolution: starting from a single die's 6 equally likely outcomes and combining one additional die's faces, 1 through 6, at a time.

Formula & Methodology

By hand, this is easiest with two dice: list all 36 equally likely combinations (6 faces x 6 faces) and count how many add up to your target sum - there's exactly 1 way to make a 2 or a 12, but 6 ways to make a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so 7 has a 6/36 = 16.667% chance. For three or more dice, the count of ways per sum grows the same way but is harder to enumerate by hand, which is where letting the calculator build the full distribution becomes useful.

Examples

Classic two-dice roll

Rolling 2 dice and targeting a sum of 7 finds 6 favorable combinations out of 36 total, for a probability of 16.667%.

Three-dice roll

Rolling 3 dice and targeting a sum of 10 finds 27 favorable combinations out of 216 total, for a probability of 12.5%.

Advantages

  • Calculates the exact probability from the full combinatorial distribution rather than estimating from a simulated sample of rolls.
  • Works for any number of dice from 1 to 6 and any target sum, not just the common two-dice case.
  • Shows both the probability and the raw ways-to-total-outcomes fraction, useful for anyone who wants to verify the math themselves.

Common Mistakes

  • Assuming every possible sum is equally likely, which is only true when rolling a single die - with two or more dice, sums near the middle of the range have far more combinations than the extremes.
  • Entering a target sum that's impossible for the number of dice chosen, such as targeting a sum of 2 with three dice when the minimum possible is 3, and misreading the resulting 0% as an error.
  • Forgetting that the probability distribution is symmetric, so a sum of 4 with two dice has the same odds as a sum of 10, which can be used as a quick sanity check.

Edge Cases to Watch For

  • The number of dice entered is rounded to the nearest whole number and capped between 1 and 6, so entering a larger dice count, like 10, is silently treated as 6.
  • A target sum outside the possible range for the chosen dice count, below the dice count itself or above 6 times the dice count, returns 0 ways and a 0% probability rather than an error.
  • Non-integer target sums are rounded to the nearest whole number before checking, since a fractional sum isn't a valid dice outcome.

Common Use Cases

  • Tabletop RPG and board game players estimating how likely a specific dice total is before committing to a strategy.
  • Game designers testing whether a dice-based mechanic produces the probability curve they intend.
  • Students or hobbyists checking combinatorics and probability distribution homework against exact computed odds.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

Why is rolling a 7 with two dice more likely than rolling a 2 or 12?

There are 6 different ways to roll a sum of 7 with two dice (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) but only 1 way each to roll a 2 (1+1) or a 12 (6+6) - sums near the middle of the possible range have more combinations of dice faces that add up to them, which is why the probability distribution peaks in the middle and tapers off toward the extremes.

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Conclusion

Because the calculation enumerates the exact combinatorial distribution rather than approximating it, the probability shown is precise, not a statistical estimate. It's a fast way to confirm intuitions about dice odds that can otherwise be easy to misjudge with three or more dice.