Dice Probability Calculator

For six dice or fewer, each with up to 20 sides, and only where the total number of possible outcomes stays under a million, it enumerates every possible combination and counts the exact fraction that meets your target. That combination cap can still be hit within the six-dice/d20 ceiling itself — 6d20 alone has 64 million combinations, well past the million-outcome limit — so some large-pool, high-sided inputs fall back to a normal-distribution approximation even though they're within the "six dice, d20 or smaller" range. The approximation is accurate near the middle of the range but slightly less precise for very extreme target numbers on a large dice pool.

Against a fixed target number, adding more dice tends to swing your odds harder, since a single die either clears the target or it doesn't while a full pool averages out toward reliability across a wider range of totals. Increasing the number of sides also raises the average roll and widens the spread, but more gradually — it changes the shape of the distribution rather than acting like an on/off switch the way pool size can.

Not directly. This tool sums a flat pool of same-sided dice plus a modifier against a target number; it does not model rolling twice and keeping the higher or lower result, which is how advantage and disadvantage work in systems like D&D 5e. You would need to run two separate single-die probability checks and combine them by hand.

The modifier is added directly to the dice total before comparing it against the target number, so a +2 modifier is mathematically identical to needing a target two points lower. It shifts your entire probability distribution up or down without changing its shape or spread — unlike adding another die, which changes the shape too.

Standard deviation measures how spread out your possible totals are, and that spread depends only on how many dice you roll and how many sides they have — not on your modifier or your target number. A flat +5 shifts every possible outcome up by 5 equally, so the spread between your luckiest and unluckiest rolls stays exactly the same.