Dice Probability Calculator

Graph probability distributions for uniform, mixed, or dropped dice pools.

Dice Settings

Count

Die Type

Modifier (+/-)

Drop / Keep Rule

Visual Probability ChartHover bar for details

Roll Statistics

Roll Range:2 – 12

Mean (Average):7.00

Std Deviation:2.415

Calculation type:Exact Math

Query Probability

P(Roll

Enter target value above

Outcome Probability Breakdown Table

Roll Result (Sum)	Outcomes	Probability (%)
2	1	2.778%
3	2	5.556%
4	3	8.333%
5	4	11.111%
6	5	13.889%
7	6	16.667%
8	5	13.889%
9	4	11.111%
10	3	8.333%
11	2	5.556%
12	1	2.778%

Understanding dice rolling probabilities

Roll distributions are calculated using successive convolutions of discrete uniform vectors representing die faces. When keeping or dropping dice (such as D&D 5e character stat generation where you roll 4d6 and keep the highest 3), the variables become dependent, requiring exact combination trees or Monte Carlo simulations.

This calculator allows modeling mixed pools (e.g. 2d6 + 1d10), applying static bonuses, and inspecting cumulative thresholds (at least/at most probabilities) via interactive charts.

Built and maintained by Meet Shah · Last updated 1 August 2026

What this tool is used for

Getting the full distribution for a sum of several dice.
Checking the odds of hitting a threshold on a roll.
Comparing two dice pools for a game design decision.
Understanding why a sum of two dice is not uniform.
Working out how likely an unlikely-feeling result actually was.

Frequently Asked Questions

Why is 7 the most likely total on two dice?: Because it has the most ways to occur — six of the 36 outcomes (1+6, 2+5, 3+4 and their reverses) against one each for 2 and 12. The distribution is triangular, and it is the clearest small demonstration that the number of combinations, not the range, decides the shape.
What happens to the shape with more dice?: It converges toward a bell curve — the central limit theorem in miniature. With three dice the peak flattens and widens; by ten the distribution is visually normal. The extremes become vanishingly unlikely: all-ones on ten d6 is one chance in over sixty million.
How does advantage in d20 systems change the odds?: Rolling twice and keeping the higher shifts the average from 10.5 to about 13.8 and makes a 15-or-better roll rise from 30% to 51%. The effect is largest in the middle of the range and smallest at the extremes, which is why it feels stronger on a moderate check than a desperate one.
Are dice rolls independent?: Yes for fair dice, and that is what makes the gambler's fallacy a fallacy — a run of sixes does not make the next roll less likely to be six. Real dice are not perfectly fair: casino dice are machined to tolerances precisely because moulded consumer dice measurably are not.
How is the probability of at least one success computed?: Through the complement: 1 − P(no successes). For four dice each with a 1/6 chance, that is 1 − (5/6)⁴ ≈ 51.8%. Adding the individual probabilities instead gives 66.7%, which double-counts the outcomes where more than one succeeds.

Common errors and gotchas

Assuming a sum of dice is uniform, when it is not — the middle values are far more likely.
Confusing the probability of at least one success with the probability of exactly one.
Adding probabilities of events that are not mutually exclusive.
Reading a run of unlikely rolls as evidence the dice are loaded, on far too small a sample.
Applying single-die intuition to a pool, where the distribution changes shape entirely.