Expected Value Calculator
Expected value of three possible outcomes, with the variance and standard deviation of the result.
Results
True or expected value
39.00000
Percentage
100.000
%
Variance (sample)
4309.0000
Standard deviation (sample)
65.6430
What this tool does
Expected value is what you would average over many repetitions, which is exactly why it is a poor guide for something you will do only once: a positive expectation with a ruinous downside is still a bad idea. Check that the probabilities add to a hundred — the second result exists to catch that. The spread beside it is what expected value alone hides.
Formula
E = Σ p × value
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p1 | Probability of the first | % |
v1 | First outcome | — |
p2 | Probability of the second | % |
v2 | Second outcome | — |
p3 | Probability of the third | % |
v3 | Third outcome | — |
EV | True or expected value | — |
SP | Percentage | % |
VR | Variance (sample) | — |
SD | Standard deviation (sample) | — |
Worked example
- Probability of the first50 %
- First outcome100
- Probability of the second30 %
- Second outcome-50
- Probability of the third20 %
- Third outcome20
- True or expected value39.00000
- Percentage100.000 %
- Variance (sample)4309.0000
- Standard deviation (sample)65.6430
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.