Dice Probability & Standard Deviation Calculator

Exact distribution, mean and standard deviation for the sum of any number of fair dice.

Step-by-step guides

• What Are the Expected Value and Standard Deviation of Dice Rolls?
  For a fair six-sided die, the expected roll is 3.5 and the standard deviation is about 1.708; for n independent rolls, use the scaling rules.
• What Is the Standard Deviation of a Dice Roll?
  The standard deviation of one fair six-sided die is √(35/12) ≈ 1.708. See the derivation, the formula for any die, and how it scales for sums and averages.

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