Math calculators

Dice Probability Calculator

Updated May 26, 2026 By Jehan Wadia
Dice Configuration
1 to 20 dice.
Enter 1–20
Enter a valid target value

Probability Result
Probability (Fraction)
5/36
Probability (Decimal)
0.138889
Probability (Percentage)
13.89%
Odds (1 in …)
1 in 7.20
Favorable / Total Outcomes
5 / 36
Probability Distribution
Summary Statistics
Detailed Probability Table
ValueFavorableProbabilityPercentageCumulative ≤Cumulative ≥

Introduction

This Dice Probability Calculator helps you find the exact chance of any dice roll outcome. Pick your dice type, choose how many dice to roll, and set a condition like "sum equals 7" or "at least one die shows a 6." The calculator instantly shows the probability as a fraction, decimal, and percentage. It also builds a full probability distribution chart and table so you can see every possible result at a glance. Whether you play board games, tabletop RPGs like D&D, or just want to learn how dice math works, this tool gives you clear and accurate answers in seconds.

How to Use Our Dice Probability Calculator

Enter your dice settings below to find the exact probability of any dice roll outcome. The calculator will show you the probability as a fraction, decimal, and percentage, plus a full distribution chart and table.

Dice Type: Pick the type of die you want to roll. Choose from standard dice like D4, D6, D8, D10, D12, or D20. Select "Custom" if you need a die with a different number of faces.

Custom Number of Faces: If you picked "Custom" as your dice type, type in how many faces your die has. The minimum is 2 faces.

Number of Dice: Enter how many dice you want to roll at once. You can roll anywhere from 1 to 20 dice.

Probability Condition: Choose what outcome you want to calculate. Options include dice sum equals, greater than, or less than a target value. You can also check if at least one die, all dice, or an exact number of dice hit a target. For D&D players, Advantage and Disadvantage modes are included.

Target Value (X): Enter the number you want to test against. For example, if you chose "Dice sum = X," type in the sum you want to find the probability for.

Number of Matching Dice (N): This field appears when you pick "Exactly N dice equal X" or "At least N dice equal X." Enter how many dice need to match your target value. This uses the same combination math (also called binomial coefficients) to count the number of ways to choose which dice match.

Click Calculate to see your results. Click Reset to clear all inputs and start over.

What Is Dice Probability?

Dice probability is the chance that a specific result will happen when you roll one or more dice. Every standard die has an equal chance of landing on each face. For example, a 6-sided die has a 1 in 6 chance of rolling any single number. When you roll multiple dice together, the number of possible outcomes grows quickly, and some totals become more likely than others. If you want to explore the average outcome of dice rolls instead, try our Dice Average Calculator.

How Dice Probability Works

To find the probability of a dice roll, you divide the number of ways your desired result can happen by the total number of possible outcomes. With one 6-sided die, there are 6 possible outcomes. With two 6-sided dice, there are 36 possible outcomes (6 × 6). A sum of 7 is the most common result with two dice because there are 6 different ways to roll it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), giving a probability of 6/36 or about 16.67%. For a deeper look at how fractions like 6/36 simplify, you can use our Fraction Calculator. Understanding general odds and probability concepts is also helpful, and our Odds Calculator can assist with converting between different probability formats.

Common Dice Types

Different games use different dice. The most common types are:

  • D4 – 4 faces, shaped like a tetrahedron
  • D6 – 6 faces, the standard cube used in most board games
  • D8 – 8 faces, shaped like an octahedron
  • D10 – 10 faces, shaped like a decahedron
  • D12 – 12 faces, shaped like a dodecahedron
  • D20 – 20 faces, shaped like an icosahedron, popular in Dungeons & Dragons

Advantage and Disadvantage

In Dungeons & Dragons, advantage means you roll two dice and keep the higher result. Disadvantage means you roll two dice and keep the lower result. Advantage makes high rolls more likely, and disadvantage makes low rolls more likely. This calculator can show you the exact probability distribution for both.

Why Dice Probability Matters

Knowing dice probabilities helps you make smarter choices in board games, tabletop RPGs, and gambling. It lets you understand which outcomes are common and which are rare. For example, if you need to roll a 12 with two 6-sided dice, the odds are only 1 in 36 (about 2.78%). Understanding these odds helps you plan your strategy and set realistic expectations for any dice-based game.

Dice probability is closely related to broader statistical concepts. The summary statistics shown in this calculator, such as mean, standard deviation, and variance, are the same measures used throughout statistics. You can explore these concepts further with our Standard Deviation Calculator or Mean Median Mode Calculator. The "Exactly N dice equal X" and "At least N dice equal X" conditions use the binomial distribution, which you can study in more detail with our Binomial Distribution Calculator. For understanding how probabilities relate to the normal bell curve as you roll more dice, our Normal Distribution Calculator and Z Score Calculator are useful references.

If you enjoy probability in gaming contexts, you might also find our Poker Odds Calculator, Blackjack Calculator, and EV Calculator helpful for calculating expected values and odds in card games. For sports betting probability, check out our Parlay Calculator. And if you need to count the number of arrangements or selections possible in a problem, our Permutation Calculator and Factorial Calculator can help with those calculations.


Frequently asked questions

What dice types can I use with this calculator?

You can use D4, D6, D8, D10, D12, and D20. You can also pick Custom and type in any number of faces from 2 to 1000.

How many dice can I roll at once?

You can roll 1 to 20 dice at the same time. Just type the number you want in the Number of Dice box.

What does the Target Value (X) mean?

The target value is the number you want to test against. For example, if you pick "Dice sum = X" and set X to 7, the calculator finds the chance that your dice add up to exactly 7.

What is the difference between 'at least one die' and 'all dice' conditions?

At least one die means only one die needs to meet the condition for success. All dice means every single die you roll must meet the condition. "All dice" is always harder to achieve than "at least one die."

What do 'Exactly N dice equal X' and 'At least N dice equal X' mean?

"Exactly N dice equal X" finds the chance that a specific number of your dice show the target value and the rest do not. "At least N dice equal X" finds the chance that N or more of your dice show the target value.

How is the probability shown?

The result is shown in three formats: a fraction (like 5/36), a decimal (like 0.138889), and a percentage (like 13.89%). You also see the odds as "1 in X" and the count of favorable versus total outcomes.

What does the probability distribution chart show?

The chart shows a bar for every possible outcome value. The height of each bar shows how likely that value is. Green bars highlight the values that match your chosen condition.

What do cumulative ≤ and cumulative ≥ mean in the table?

Cumulative ≤ is the chance of rolling that value or less. Cumulative ≥ is the chance of rolling that value or more. These help you see the odds of a range of outcomes at once.

Why is 7 the most common sum with two six-sided dice?

There are 6 ways to make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total outcomes. No other sum has as many combinations, so 7 has the highest probability at about 16.67%.

Can I use this calculator for games other than D&D?

Yes. This calculator works for any game that uses dice, including board games like Monopoly, Yahtzee, Craps, Warhammer, and any other tabletop or dice game. Just pick your dice type and number of dice.

What are the summary statistics and what do they tell me?

The summary statistics include mean (the average roll), standard deviation (how spread out the results are), variance, median (the middle value), and mode (the most common value). These help you understand the overall shape and center of your dice outcomes.

Why does the calculator cap at 20 dice?

Rolling more than 20 dice creates a very large number of possible outcomes. The calculator limits dice to 20 so it can give you fast and accurate results without slowing down your browser.

What happens if my target value is impossible?

The calculator will show a probability of 0. For example, if you roll two D6 dice and set the target sum to 1, that result cannot happen, so the probability is 0%.

Does each face of a die have an equal chance of landing?

Yes. This calculator assumes every die is fair, meaning each face has the exact same chance of being rolled. For a D6, each face has a 1 in 6 chance.

Can I use a keyboard shortcut to calculate?

Yes. Press Enter while your cursor is in any input field or dropdown, and the calculator will run automatically.