How to use it
- Type one outcome per line: its value, a semicolon, then its chance in percent, for example 40; 20.
- Check that the Sum of the chances is 100%. The check below it turns red if not.
- Read Expected value and the Contributions table, which shows what each outcome adds.
- Open Working to see each multiplication and the total.
How the expected value is calculated
The expected value of a list of outcomes is the average result over many repetitions, with each outcome counted as often as its chance. You multiply each outcome by its chance and add the results.
The chances are typed in percent, so the contribution of one outcome is its value multiplied by its chance, divided by 100. The open probability notes used for this are listed in the sources.
E[X] = Σ x × P(X = x)
P(X = x) = chance in percent ÷ 100Why the chances must add up to 100%
- Every possible outcome must be on the list once, so the chances of all of them add up to 100%.
- If they add up to less, an outcome is missing. If they add up to more, a chance is counted twice. Then the expected value is not a true average, and the check says so.
What this calculator does not cover
- Outcomes that are not numbers, and continuous outcomes such as a time measured to the second.
- Chances that depend on one another or change over time.
- Risk, utility or any decision based on the expected value.
Worked example: daily sales of a shop
A shop sells 40 units on 20% of days, 60 units on 50% of days and 90 units on 30% of days. The contributions are 40 × 20% = 8, 60 × 50% = 30 and 90 × 30% = 27.
Added together, 8 + 30 + 27 = 65. On an average day the shop sells 65 units, and the three chances add up to 100%.
| Result | Value |
|---|---|
| Expected value | 65 |
| Sum of the chances | 100.00% |
Frequently asked questions
What does the expected value mean?
It is the average result over a very large number of repetitions, with each outcome counted as often as its chance. It is not always a value the outcome can take: 65 units is an average, not what a single day sells.
Do I type the chance as a percentage or as a decimal?
As a percentage: type 20 for 20%. The calculator divides by 100 for you. If your chances are decimals such as 0.2, multiply them by 100 first.
Why does the check say the chances do not add up?
The list is missing an outcome, or it lists one twice, or a chance is wrong. Correct the list. The expected value is a true average only when the chances add up to 100%.
Can I use a decimal comma?
No. In English a comma separates the numbers on a line, so write 2.5 for two and a half. The Turkish page reads the comma as the decimal mark.
Does the calculator send my numbers anywhere?
No. Everything is calculated in your browser, and nothing you enter is stored or sent to us.
Sources
Figures and text last checked on Thursday, November 12, 2026.