Expected Value Calculator

Enter a set of outcomes with their values and probabilities to get the expected value, variance and standard deviation. Weights are normalised for you. Calculates in your browser.

Format: value, probability. Probabilities can be fractions (0.25) or raw weights, they're normalised automatically.

Expected value

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Standard deviation-
Variance-
Probability total-

Show the math

Expected value is the long-run average: each outcome's value weighted by its probability, summed up.

EV = Σ (value × probability)

Variance measures spread (the average squared distance from the EV) and its square root is the standard deviation.

All math runs locally in your browser.

What this does

An expected value calculator takes a set of outcomes with values and probabilities and returns the expected value, variance, and standard deviation.

How to use it

  1. Enter each outcome value.
  2. Enter its probability or weight.
  3. Add as many outcomes as needed.
  4. Read the EV and spread.

How it works

Each value is weighted by its probability and summed. Raw weights are normalised for you, so they need not add to one.

EV = Σ (value × probability)

Understanding your result

Expected value is the long-run average per attempt, so a positive number favours you over many repetitions but says nothing about any single try. Read the standard deviation alongside it: a high spread means individual results swing wildly around that average, so a positive EV with huge variance can still bankrupt you before the long run arrives.

Example

A 50/50 bet of +10 or −10 has an expected value of 0.

Sources & methodology

Last updated .

Frequently asked questions

What is expected value?

The long-run average outcome, each value weighted by its probability and summed.

Do probabilities need to add to one?

No. You can enter raw weights and they are normalised automatically.

Is my data kept?

No. Everything is computed locally in your browser.