ReadyCalculator
MathPhysicsFinanceConstructionBiologyChemistryConversionEcologyEveryday LifeFoodHealthSportsStatisticsOther

Dice Average Calculator

Enter how many dice you roll and how many sides each die has. The calculator returns the expected total, variance, and standard deviation of the roll.

Expected Total

7.00

E[X] for 2d6

Variance

5.83

σ² of the total

Std. Deviation

2.42

σ of the total

Rolling 2d6 has an expected total of 7.00 with possible outcomes from 2 to 12.

How to Use This Calculator

  1. Enter the number of identical dice you plan to roll.
  2. Specify how many equally likely faces each die has (e.g., 6 for a standard die).
  3. Review the expected total, variance, and standard deviation for the combined roll.
  4. Use the range to understand the minimum and maximum possible outcomes.

Formula

E[die] = (1 + s) / 2

Var[die] = (s² − 1) / 12

E[total] = n · E[die]

Var[total] = n · Var[die]

These formulas assume fair dice with outcomes 1 through s. Because the dice are independent, expectations and variances add.

Full Description

Dice games rely on expected values to evaluate strategies. Knowing the average outcome of a roll helps you judge risk and reward across board games, tabletop RPGs, or probability exercises. Because each die is uniform, the expected value is simply the midpoint between the smallest and largest face. Adding more dice multiplies the expectation while also increasing variance.

The variance and standard deviation quantify spread: more dice smooth out the distribution, making extreme totals less likely. Use these metrics to compare different dice pools and understand how random variation affects gameplay.

Frequently Asked Questions

Can I mix dice with different sides?

This calculator assumes all dice are identical. For mixed dice, compute each die's expectation separately and add the results.

What happens with loaded dice?

Loaded dice break the uniform assumption. You would need the probability of each face to compute a weighted expectation instead of using (s + 1)/2.

Why does variance matter?

Variance indicates how spread out the totals are. High variance means more volatility; low variance implies more consistent outcomes around the mean.

Can I use this for percentile dice?

Yes. Set sides per die to 100 for a d100, or to 10 if you roll two d10s and interpret one as tens and the other as ones.