Calculadora de Probabilidade de Dados
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
enumerativo para N ≤ 4, aprox. normal com μ=3,5N e σ²=35N/12 para N maior
About this calculator
The Dice Probability Calculator determines the chance of obtaining a specific sum when rolling a given number of six-sided dice. For few dice (up to 4), the calculation is exact via enumeration of all possible combinations. For more dice (from 5 onward), the tool uses a normal approximation, which becomes quite accurate for 10 or more dice. This allows estimating probabilities even with many dice, where enumeration would be impractical.
The operation is based on probability theory. For up to 4 dice, the calculator counts the number of ways to achieve the desired sum and divides by the total possible outcomes (6 raised to the number of dice). For 5 or more dice, it uses the normal approximation: the sum follows an approximately normal distribution with mean equal to 3.5 times the number of dice and variance equal to 35/12 times the number of dice. The calculator computes the Z-score and obtains the cumulative probability.
You can use this calculator in various situations, such as board games (Risk, Dungeons & Dragons), gambling analysis, or understanding probability concepts in the classroom. For example, when rolling 3 dice, what is the chance of summing exactly 10? Or, with 20 dice, what is the probability the sum exceeds 70? The tool answers quickly.
Cautions: the normal approximation is continuous, while the sum of dice is discrete. To improve accuracy, it is recommended to use a continuity correction (subtract or add 0.5 to the sum value). Additionally, the approximation is less accurate for extreme values (tails) or few dice; for 5 to 9 dice, the result is approximate. Always check if the number of dice is suitable for the chosen method.
Frequently asked questions
What is the difference between the exact method and the normal approximation?
The exact method counts all possible combinations and is used for up to 4 dice, giving a precise result. The normal approximation is a statistical formula that estimates the probability for 5 or more dice, being very good for 10 or more.
Do I need to use continuity correction?
Yes, to improve the accuracy of the normal approximation, it is recommended to use continuity correction: when calculating the probability of an exact sum S, consider the interval from S-0.5 to S+0.5.
How many dice can I calculate?
The calculator accepts any number of dice, but the exact method only works up to 4. For more dice, it uses the normal approximation. The result is reliable for 10 or more dice.
Does this calculator work for other types of dice?
No, it is specific to six-sided dice (1 to 6). For dice with other numbers of faces, the mean and variance would be different.
How do I interpret the result?
The result is the probability of obtaining the exact sum entered. For example, 0.15 means a 15% chance. If approximation was used, the value is approximate.