Expected Value Calculator
Calculate the expected value, variance, and standard deviation of a discrete random variable. Enter each possible outcome with its value and probability.
Recommended Settings
Pro Tips
- •Expected value is the weighted average of all possible outcomes, weighted by how likely each one is
- •Probabilities should be entered as decimals between 0 and 1 (for example, 25% is 0.25) and should sum to 1 across all outcomes
- •Variance and standard deviation measure how spread out the outcomes are around the expected value
- •A negative expected value in a game or bet means that, on average, you'd expect to lose money over many repetitions
Most Popular
Most users model a simple bet or game with 2-4 possible outcomes and their probabilities
When to Use This Tool
Calculate the expected value of a discrete random variable for a statistics or probability course.
Estimate the average outcome of a bet or game given its payouts and probabilities.
Evaluate the expected outcome of a decision with multiple possible results and known probabilities.
Compare the expected value of different choices to inform a decision under uncertainty.
How It Works
Multiply each outcome's value by its probability
Sum those products together to get the expected value
Calculate variance by weighting each outcome's squared distance from the expected value by its probability
Take the square root of the variance to get the standard deviation
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Files never leave your device. All processing happens locally in your browser.
Lightning Fast
Powered by Client-side JavaScript probability calculations for optimal performance on modern browsers.
Open Source
Built with verified, open-source libraries. Fully transparent.
Frequently Asked Questions
What does expected value actually mean?
Expected value represents the long-run average outcome if you repeated the same random process many times. It's not necessarily a value that can actually occur - for example, a die roll's expected value is 3.5, even though you can never roll a 3.5.
Why do my probabilities need to sum to 1?
Probabilities represent the full set of possible outcomes, so they must account for 100% of the possibilities. If they sum to something other than 1, the calculation is based on an incomplete or invalid distribution.
What does a negative expected value mean?
In the context of a bet or game, a negative expected value means that, on average, you'd expect to lose money over many repetitions - the losses outweigh the wins when weighted by their probabilities.
Is my data sent to a server?
No. All calculations happen instantly in your browser using JavaScript. Nothing you enter is transmitted anywhere.
How is variance different from standard deviation?
Variance measures spread in squared units of the original value, which can be hard to interpret directly. Standard deviation is the square root of variance, bringing it back to the same units as the original values, making it easier to interpret.