Work out the probability of a dice roll for any number of dice with any number of sides. Choose your dice, pick a condition — a target sum, matching values, all high or low, or a Dungeons & Dragons advantage roll — and get the exact odds as a percentage, a decimal, and a fraction.
The dice probability calculator tells you how likely a particular dice roll is, across a huge range of situations. Whether you are rolling a single classic six-sided die, a fistful of twenty-sided dice for a tabletop campaign, or any custom die you can imagine, this tool computes the exact probability of the outcome you care about. It handles totals (the sum of all the dice), matching values (how many dice show a specific number), "all high" or "all low" conditions, and even the advantage and disadvantage rolls used in Dungeons & Dragons. Results are shown as a percentage, a decimal, and a reduced fraction so you can read them however you like.
Dice are the beating heart of countless board games, role-playing games, and games of chance, and understanding the odds behind them turns guesswork into strategy. This page walks through every type of dice probability the calculator can find, the formulas behind each one, worked examples you can reproduce, and answers to the questions players ask most.
While the six-sided cube is the die most people picture, games use many shapes. A standard Dungeons & Dragons set contains seven polyhedral dice, and this calculator supports all of the common ones plus any custom number of sides:
Every face of a fair die is equally likely, so on a die with s sides the chance of any specific face is 1/s. That single fact is the foundation of every calculation on this page.
Two ideas do most of the heavy lifting. First, for a single fair die with s sides, each outcome has probability 1/s — so a six-sided die gives 1/6 for any chosen number. Second, separate dice are independent: the result of one die has no effect on another. To find the probability that several independent events all happen, you multiply their individual probabilities. Rolling two sixes on two dice is therefore (1/6) × (1/6) = 1/36. When you want the probability of "this or that" mutually exclusive outcome, you instead add the probabilities. Nearly every dice question is built from these two operations, sometimes combined with counting techniques like combinations.
Asking for the probability that several dice add up to a particular total is one of the most common questions — and one of the most interesting, because the totals are not equally likely. With two six-sided dice there are 6 × 6 = 36 equally likely ordered outcomes. A total of 7 can be made six ways: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), so its probability is 6/36 = 1/6 ≈ 16.67%. A total of 2, by contrast, can only be made one way, (1,1), giving 1/36 ≈ 2.78%. This is why 7 is the most common roll in games like craps and Monopoly, and why the totals form a triangular, bell-like shape peaking in the middle. The calculator finds these probabilities for any number of dice and sides by counting every combination that produces the target total and dividing by the total number of possible rolls.
Often you do not need an exact total but a threshold — "at least 10" to succeed, or "at most 4" to fail. The calculator adds up the probabilities of every qualifying total. For two six-sided dice, a sum of at least 10 covers totals of 10, 11, and 12, which occur in 3 + 2 + 1 = 6 ways, giving 6/36 = 1/6 ≈ 16.67%. A sum of at most 4 covers 2, 3, and 4, occurring in 1 + 2 + 3 = 6 ways — also 1/6. These cumulative probabilities are exactly what you want when a game rule says "roll X or higher."
Some conditions apply to every die at once. The calculator handles three:
When you want a certain number of dice to show a specific face — say exactly two sixes among five dice — the calculation uses the binomial distribution. Each die is a success (shows the target value, probability p = 1/s) or a failure (anything else, probability 1−p). The chance of exactly k successes in n dice is:
P(X = k) = C(n, k) × pk × (1 − p)n−k
where C(n, k) is the number of ways to choose which k dice succeed. For example, the chance of exactly one six on two d6 is C(2,1) × (1/6) × (5/6) = 10/36 ≈ 27.8%. The "at least X" option adds up the exact probabilities from X successes all the way up to n, so "at least one six on two dice" is 1 − (5/6)2 = 11/36 ≈ 30.6%.
In fifth-edition Dungeons & Dragons, many rolls are made with advantage or disadvantage on a twenty-sided die. With advantage you roll two d20 and keep the higher result; with disadvantage you roll two and keep the lower. This calculator's D&D option finds the chance of meeting or beating a target number (a "DC") under each condition. A normal roll succeeds with probability (21−Y)/20. Advantage succeeds unless both dice fail, giving 1 − ((Y−1)/20)2, while disadvantage succeeds only if both dice clear the target: ((21−Y)/20)2. For a target of 4, a normal roll succeeds 85% of the time, advantage jumps to 97.75%, and disadvantage drops to 72.25% — a dramatic illustration of how powerful advantage is.
Probability can be expressed several ways, and each is useful in different settings. A decimal between 0 and 1 (like 0.1667) is the raw probability and the easiest to plug into further math. A percentage (16.67%) is the most intuitive for most people. Odds, often written as "1 in 6" or "5 to 1 against," are popular in gaming and gambling. The calculator gives you the percentage and decimal for every result, plus an exact reduced fraction where it is practical, so you can quote whichever form fits your game or conversation.
Understanding these odds pays off far beyond the classroom. Tabletop role-players use them to weigh risky actions and build characters. Board-game strategists use them to decide when to press their luck. Game designers rely on them to balance mechanics so that outcomes feel fair and exciting. Students meet them as a friendly introduction to probability theory, combinations, and the binomial distribution. And anyone playing a game of chance benefits from knowing the true likelihood of a roll rather than trusting a gut feeling — which is often badly mistaken, since people tend to overestimate rare events and underestimate common ones.
The single most important idea in dice probability is independence. Two dice are independent because the number showing on one has absolutely no bearing on the number showing on the other — dice have no memory, and a run of sixes does not make the next six any more or less likely. When events are independent, the probability that they all happen is the product of their separate probabilities. That is why rolling two specific numbers on two dice is (1/6) × (1/6) = 1/36, and why "all dice at least 3" becomes a probability raised to the power of the number of dice. This multiplication rule is what lets the calculator scale effortlessly from two dice to twenty. It is also the source of a famous gambler's error: believing that a result is "due" after a dry spell. Each roll starts fresh, and the odds reset completely every time the dice leave your hand. Understanding this protects you from chasing losses and helps you read every probability on this page correctly.
When you roll a single die, every outcome is equally likely, producing a flat, uniform distribution. But the moment you add a second die, the picture changes dramatically. Middle totals can be reached by many different combinations, while extreme totals can be reached by only one or two, so the probabilities form a triangle that peaks in the center — the classic result that 7 is the most common total on two six-sided dice. Add a third, fourth, or fifth die and that triangle smooths into a rounded, bell-shaped curve that looks increasingly like the normal distribution studied in statistics. This is a hands-on demonstration of the central limit theorem, which says that the sum of many independent random values tends toward a bell curve regardless of the shape you started with. It also has practical consequences for game design: totals near the middle of the range are reliable, while the extremes are rare and dramatic, which is exactly why many games reward or penalize those rare rolls so heavily. Exploring different dice counts in the calculator is a quick way to see this transformation for yourself.
There are six ways to make 7 out of 36 equally likely outcomes, so the probability is 6/36 = 1/6, or about 16.67%. It is the most likely total on two six-sided dice.
Count how many combinations of the dice produce the target sum, then divide by the total number of possible rolls (sides raised to the power of the number of dice). The calculator does this counting for you for any dice.
On two dice, "doubles" means both show the same value. There are 6 ways out of 36, so the probability is 6/36 = 1/6, the same as (1/6)^(2−1).
Advantage (roll two d20, keep the higher) increases your chance of meeting most targets by roughly 20–25 percentage points in the middle of the range, equivalent to about a +5 bonus. Disadvantage lowers it by a similar amount.
No. With one die every face is equally likely, but with two or more dice the middle totals have many more combinations than the extremes, so they are far more common. This creates the familiar bell-shaped distribution.
Yes. Choose one of the standard polyhedral dice or select Custom and enter any number of sides, from a two-sided coin-die upward. The formulas work for any fair die.
This Dice Probability Calculator is provided for general informational and educational purposes and assumes fair, independent dice where every face is equally likely. Real dice may be slightly biased. Results describe theoretical probabilities, not guaranteed outcomes of any particular set of rolls.