Expected Value Calculator
List the possible outcomes, their values and their chances to get the expected value, the long-run average, with the spread and the chance of a loss.
A name (optional), the value and its chance, as a percentage (20%) or a decimal (0.2). Use a minus sign for losses.
Expected value
13,500
- Standard deviation
- 19,371.3706
- Chance of a loss
- 30%
On average, each time this plays out it's worth 13,500. Single results can be far from that: the standard deviation is 19,371.37.
How it's worked out
- Big order
50,000 × 0.210,000 - Small order
10,000 × 0.55,000 - No order
-5,000 × 0.3-1,500 - Expected value
add them up13,500 - Standard deviation
√(sum of chance × (value − expected value)²)19,371.3706
Outcomes
| Outcome | Value | Chance | Value × chance |
|---|---|---|---|
| Big order | 50,000 | 20% | 10,000 |
| Small order | 10,000 | 50% | 5,000 |
| No order | -5,000 | 30% | -1,500 |
- Expected value is the long-run average over many repeats. For a one-off decision, also weigh how bad the worst outcome would be.
How it is worked out
Expected value = Σ value × chance. The standard deviation is the square root of Σ chance × (value − expected value)². The chance of a loss adds up the chances of all outcomes below zero.
Questions people ask
What is the expected value of 50,000 at 20%, 10,000 at 50% and −5,000 at 30%?
13,500: 50,000 × 0.2 + 10,000 × 0.5 − 5,000 × 0.3.
What is expected value?
The average result you'd get if the same situation played out many times: each outcome's value times its chance, all added up.
Do the chances have to add up to 100%?
Yes. Every possible outcome needs to be listed, so their chances total 100%.
What does the standard deviation tell me?
How far single results tend to land from the expected value. A large one means a risky choice, even if the average looks good.
About this calculator
Formula and rules last checked 10 November 2026Written and tested by the CalculatorDex teamReport a problem