Expected Value Calculator

Compute expected value, variance, and standard deviation for up to 20 weighted outcomes.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

Number of Outcomes

Outcome 1

Outcome 1 Value

Outcome 1 Probability

Outcome 2

Outcome 2 Value

Outcome 2 Probability

Outcome 3

Outcome 3 Value

Outcome 3 Probability

Outcome 4

Outcome 4 Value

Outcome 4 Probability

Outcome 5

Outcome 5 Value

Outcome 5 Probability

Outcome 6

Outcome 6 Value

Outcome 6 Probability

Outcome 7

Outcome 7 Value

Outcome 7 Probability

Outcome 8

Outcome 8 Value

Outcome 8 Probability

Outcome 9

Outcome 9 Value

Outcome 9 Probability

Outcome 10

Outcome 10 Value

Outcome 10 Probability

Outcome 11

Outcome 11 Value

Outcome 11 Probability

Outcome 12

Outcome 12 Value

Outcome 12 Probability

Outcome 13

Outcome 13 Value

Outcome 13 Probability

Outcome 14

Outcome 14 Value

Outcome 14 Probability

Outcome 15

Outcome 15 Value

Outcome 15 Probability

Outcome 16

Outcome 16 Value

Outcome 16 Probability

Outcome 17

Outcome 17 Value

Outcome 17 Probability

Outcome 18

Outcome 18 Value

Outcome 18 Probability

Outcome 19

Outcome 19 Value

Outcome 19 Probability

Outcome 20

Outcome 20 Value

Outcome 20 Probability

What This Calculator Does

This calculator treats a list of outcomes as a discrete probability distribution, normalizes the probabilities when needed, and reports the mean and spread of the resulting payoff distribution. It is useful for comparing risky choices on both return and volatility.

It combines Number of Outcomes, Outcome 1 Value, Outcome 1 Probability, Outcome 2 Value to estimate Expected Value, Variance, Standard Deviation.

Formula & Method

Core equations: E[X]=\sum x_ip_i,\quad Var(X)=\sum p_i(x_i-E[X])^2,\quad \sigma=\sqrt{Var(X)}.

Notation used in the formulas: R = Expected Value; x_{1} = Number of Outcomes; x_{2} = Outcome 1 Value; x_{3} = Outcome 1 Probability; x_{4} = Outcome 2 Value; x_{5} = Outcome 2 Probability; x_{6} = Outcome 3 Value.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you have a finite menu of possible payoffs with associated probabilities and want to understand both the average result and how dispersed those results are around the mean.

Inputs Used

Number of Outcomes: Used directly in the calculation.
Outcome 1 Value: Used directly in the calculation.
Outcome 1 Probability: Used directly in the calculation.
Outcome 2 Value: Used directly in the calculation.
Outcome 2 Probability: Used directly in the calculation.
Outcome 3 Value: Used directly in the calculation.
Outcome 3 Probability: Used directly in the calculation.
Outcome 4 Value: Used directly in the calculation.
Outcome 4 Probability: Used directly in the calculation.
Outcome 5 Value: Used directly in the calculation.
Outcome 5 Probability: Used directly in the calculation.
Outcome 6 Value: Used directly in the calculation.
Outcome 6 Probability: Used directly in the calculation.
Outcome 7 Value: Used directly in the calculation.
Outcome 7 Probability: Used directly in the calculation.
Outcome 8 Value: Used directly in the calculation.
Outcome 8 Probability: Used directly in the calculation.
Outcome 9 Value: Used directly in the calculation.
Outcome 9 Probability: Used directly in the calculation.
Outcome 10 Value: Used directly in the calculation.
Outcome 10 Probability: Used directly in the calculation.
Outcome 11 Value: Used directly in the calculation.
Outcome 11 Probability: Used directly in the calculation.
Outcome 12 Value: Used directly in the calculation.
Outcome 12 Probability: Used directly in the calculation.
Outcome 13 Value: Used directly in the calculation.
Outcome 13 Probability: Used directly in the calculation.
Outcome 14 Value: Used directly in the calculation.
Outcome 14 Probability: Used directly in the calculation.
Outcome 15 Value: Used directly in the calculation.
Outcome 15 Probability: Used directly in the calculation.
Outcome 16 Value: Used directly in the calculation.
Outcome 16 Probability: Used directly in the calculation.
Outcome 17 Value: Used directly in the calculation.
Outcome 17 Probability: Used directly in the calculation.
Outcome 18 Value: Used directly in the calculation.
Outcome 18 Probability: Used directly in the calculation.
Outcome 19 Value: Used directly in the calculation.
Outcome 19 Probability: Used directly in the calculation.
Outcome 20 Value: Used directly in the calculation.
Outcome 20 Probability: Used directly in the calculation.

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