numvana

Dice Probability Calculator

Find the exact probability of rolling a specific sum, or at least/at most that sum, with any number of same-sided dice.

P(sum = 7)
16.667% (6 / 36)
P(sum ≥ 7)
58.333%
P(sum ≤ 7)
58.333%
Possible sum range
2 – 12

How it works

Every one of numSides^numDice ways the dice can land is equally likely, so an exact probability just counts how many of those outcomes add up to the target sum. Rather than enumerating every outcome directly, this builds up the count for each possible sum one die at a time — a standard dynamic-programming convolution that gives the exact same counts a full enumeration would, just far faster.

Alongside the exact probability of hitting the target sum, it also reports the probability of the sum being at least or at most that target, by adding up the counts for every sum in that direction — useful for questions like 'what's the chance of rolling 7 or higher.'

FAQ

Why does 7 come up so often with two six-sided dice?

7 is the only sum reachable six different ways with two d6 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) — more than any other sum — because it sits at the exact middle of the 2-12 range where the most combinations overlap. Sums near either end (2 or 12) have only one way to happen.

Is this the same as simulating a lot of dice rolls?

No — this counts every possible outcome exactly using combinatorics, so the probabilities are exact fractions, not an approximation that improves with more simulated rolls. A simulation would converge toward these same numbers given enough rolls, but never quite match them exactly.

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