Expected Value Calculator
The Expected Value Calculator multiplies each value in your list by its matching probability and adds the products to return the expected value E(X), along with the sum of the probabilities you entered.
What this calculator does
The Expected Value Calculator estimates your result instantly from the values you enter, using standard statistics formulas. The Expected Value Calculator multiplies each value in your list by its matching probability and adds the products to return the expected value E(X), along with the sum of the probabilities you entered. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Expected Value Calculator
Give this tool a list of possible outcome values and the probability of each, and it returns the expected value: the probability-weighted average of the outcomes. It also totals your probabilities so you can confirm they are consistent.
The two lists must be the same length, and the probabilities should add up to 1 within a small tolerance.
Formula & Mathematical Calculation
Expected Value E(X) = f(Values (comma-separated), Probabilities (comma-separated))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
For values 10, 20, 30 with probabilities 0.2, 0.5, 0.3, the probabilities sum to 1. The expected value is E(X) = (10 × 0.2) + (20 × 0.5) + (30 × 0.3) = 2 + 10 + 9 = 21.
The tool displays Expected Value E(X) = 21 and a Sum of Probabilities of 1.
Key Benefits
- Computes the probability-weighted average of any discrete outcome list
- Totals your probabilities so you can check they sum to 1
- Works with any equal-length pair of value and probability lists
- Shows both the expected value and the probability sum at once
How to Use this Calculator
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Enter the values
Type your outcome values into the Values field, separated by commas. -
Enter the probabilities
Type the probability of each outcome into the Probabilities field, in the same order and count. -
Calculate
Press Calculate and read the Expected Value E(X) and Sum of Probabilities boxes.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Expected Value Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.