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Expected Value Calculator
The expected value is the probability-weighted average outcome — the result you can expect “on average.” Multiply each value by its probability and add them up (Expected Value = Σ (value × probability)). For a die, that is (1+2+3+4+5+6) ÷ 6 = 3.5.
Enter a value and its probability (%) per row. When probabilities sum to exactly 100, the expected value and other statistics are calculated automatically.
| Value | Probability (%) | |
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Probabilities must total exactly 100%
Rows with empty values are ignored
Enter a value and how many times it occurs (frequency) per row. The tool calculates each probability from the total frequency, then computes the expected value.
| Value | Frequency | |
|---|---|---|
| ✖ | ||
| ✖ | ||
| ✖ |
Rows with empty values are ignored
Enter a value and its probability as a fraction (e.g. 1/6) per row. When fractions sum to exactly 1, the expected value and other statistics are calculated automatically.
| Value | Probability (a/b) | |
|---|---|---|
| / | ✖ | |
| / | ✖ | |
| / | ✖ |
Fractions must sum to exactly 1
Rows with empty values are ignored
Enter a value and its probability (%) as a pair. The expected value is calculated once probabilities sum to exactly 100. Use “Fill Remaining” to auto-fill the last empty probability field.
Enter a value and the number of times it occurs. The tool uses the total of all frequencies as the denominator to compute each probability, then calculates the expected value. Useful for tallying dice rolls or survey data.
Enter a value and its probability as a fraction (e.g. 1/6). The expected value is calculated once all fractions sum to exactly 1. Use “Fill Remaining” to auto-calculate the remaining probability.
- Expected ValueThe probability-weighted average outcome. Calculated as the sum of each value multiplied by its probability.
- SumThe total of all entered values (probability not considered).
- AverageThe simple arithmetic mean of the entered values (probability not considered).
- VarianceA measure of how spread out the values are around the expected value. Higher variance means greater spread.
- Std DevThe square root of variance. Expresses spread in the same units as the expected value.
How do you calculate expected value?
Multiply each outcome’s value by its probability, then add them all up (Expected Value = Σ (value × probability)). This tool does it automatically once you enter the values with their probabilities, frequencies, or fractions.
What’s the difference between expected value and average?
A simple average treats every value equally, while the expected value weights each value by how likely it is to occur. When all outcomes are equally likely, the two are the same.
Why is a die’s expected value 3.5?
Each face from 1 to 6 appears with probability 1/6, so (1+2+3+4+5+6) ÷ 6 = 3.5. No face shows 3.5, but it is the value you can expect on average.
What are variance and standard deviation?
Variance measures how far the outcomes spread from the expected value, and standard deviation is its square root, expressed in the same units. Larger values mean less predictable results.