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Dice Probability Calculator

Find the odds of rolling a given sum with multiple dice.

How it is calculated

The tool gives the chance that n fair dice with s sides each add up to exactly your target total t. It counts the ordered ways to reach t, building the count die by die, then computes probability = ways ÷ sn × 100. The denominator sn is the number of equally likely outcomes. It also shows the number of ways and that total; once either passes about 9 × 1015 it is printed in scientific notation (50 dice of 1000 sides: total 1.0000 × 10150). The probability is not affected. Dice must be from 1 to 50, sides from 2 to 1000, and decimals are cut to whole numbers. A target below n (every die shows at least 1) or above n × s is impossible and returns 0%. The result is for exactly that total, not for "at least" or "at most"; for those you add the probabilities of the totals involved.

Worked example

Roll three six-sided dice and ask for a total of 10. Step 1: the number of equally likely outcomes is 6³ = 216. Step 2: counting the ordered rolls that add to 10 gives 27 ways (for example 1-3-6 can appear in 6 orders, 4-3-3 in 3). Step 3: 27 ÷ 216 = 0.125, so the probability is 12.50%, about 1 chance in 8.

Try this example →

Common mistakes

  • Counting 4-3-3 and 3-4-3 as the same roll; the tool counts ordered outcomes because each die is separate, so these are different ways.
  • Expecting "10 or more": the tool gives the chance of exactly 10 only.
  • Entering the number of faces of a die as the number of dice, or swapping the two fields.
  • Assuming all totals are equally likely with several dice; the middle totals are much more common than the extremes.
  • Forgetting that dice that are rerolled, exploded or dropped (as in some tabletop systems) follow different rules.

About this calculator

This calculator computes the exact probability of rolling a specific total with any number of dice and any number of sides, by counting the outcomes that sum to the target out of all possible outcomes (sides raised to the number of dice) — the same combinatorics behind the classic 2d6 bell curve where 7 is the most likely roll.

Board game and tabletop RPG players, game designers balancing dice mechanics, and probability students use it to see which totals are common versus rare.

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Comments (1)

  • Editorial team

    For a quick feel, the most likely total sits in the middle of the range, and the odds fall away toward both ends. With three six-sided dice, 10 and 11 tie as the commonest results at 12.50% each. To get an at-least figure, add several exact results by hand: 15 or higher on 3d6 is 10, 6, 3 and 1 ways for totals 15 to 18, so 20 out of 216, about 9.26%. Which dice mechanic are you trying to price?

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