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Dice Expected Value Calculator

Expected sum and variance for N · dS dice.

Compute the expected value and variance of rolling N identical fair dice (each with S sides), using E = N · (S+1)/2 and Var = N · (S² − 1)/12.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

E = N · (S+1) / 2; Var = N · (S² − 1) / 12; SD = √Var.

In depth

Compute the expected value and variance of rolling N identical fair dice (each with S sides), using E = N · (S+1)/2 and Var = N · (S² − 1)/12.