Dice Probability Calculator

Calculating probabilities for dice outcomes looks simple until you roll more than one die. Suddenly, the number of combinations explodes, making it time-consuming to do it manually.

Our Dice Probability Calculator makes this effortless by instantly computing the probability for:

• The sum of all dice equals an exact value.
• The sum of all dice is at least a value.
• The sum of all dice is at most a value. 

What Is Dice Probability?

Dice probability refers to the likelihood of achieving a specific result when rolling one or more dice. The probability depends on:

• Number of sides on each die (s)
• Number of dice rolled (n)
• Target sum or condition (exact sum, at least, at most)

Dice Probability Formulae

To compute dice probability, we determine:

• How many combinations produce the target sum or meet the condition, and
• Divide that count by the total number of outcomes.

$$P\left(\text{Event}\right)=\frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}}$$

For n dice with s sides, the total number of outcomes is:

Total Outcomes = sⁿ

For the below formulae:
n = No. of dice
s = No. of individual die faces
T = Target Sum

Probability That the Sum of All Dice Equals a Target Sum (Exact Sum)

Probability That the Sum of All Dice Is At Least a Target Sum

$$P\left(\text{Sum ≥}T\right)=\sum _{x=T}^{ns}P\left(\text{Sum =}x\right)$$

Where:
ns = maximum possible sum

Probability That the Sum of All Dice Is At Most a Target Sum

$$P\left(\text{Sum ≤}T\right)=\sum _{x=n}^{T}P\left(\text{Sum =}x\right)$$

Where:
n = minimum possible sum

How to find Dice Probability using our Calculator?

1. Select the type of dice, i.e., No. of sides in a die.
2. Enter the number of dice and target sum.
3. Click “Calculate” and the calculator automatically computes the desired results.