Probability Distribution Calculator
Enter a list of values and their matching probabilities to get the mean, variance and standard deviation of the discrete probability distribution. The probabilities should sum to about 1.
What this calculator does
The Probability Distribution Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Enter a list of values and their matching probabilities to get the mean, variance and standard deviation of the discrete probability distribution. The probabilities should sum to about 1. 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 Probability Distribution Calculator
This calculator summarizes a discrete probability distribution. Enter your outcome values and the probability of each, and it returns the distribution's mean (μ), variance (σ²) and standard deviation (σ).
Use it when each outcome has a known probability and you want the expected value and spread. The probabilities must add up to roughly 1 (within a small tolerance) or the tool will ask you to correct them.
Formula & Mathematical Calculation
Mean μ = f(Values (comma-separated), Probabilities (comma-separated))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
Enter Values of 1, 2, 3 and Probabilities of 0.2, 0.5, 0.3, then click Calculate.
The tool returns Mean μ = 2.1, Variance σ² = 0.49 and Std. Dev. σ = 0.7, with the note: “Distribution mean μ = 2.1, variance = 0.49, standard deviation = 0.7.”
Key Benefits
- Computes the mean, variance and standard deviation of a discrete distribution in one step
- Checks that the probabilities sum to about 1 and reports the current total if they do not
- Takes value and probability lists as simple comma-separated input
- Rounds each of the three summary statistics to four decimal places
How to Use this Calculator
-
Enter the values
Type the possible outcome values into the Values field, separated by commas, for example 1, 2, 3. -
Enter the probabilities
Type each outcome's probability into the Probabilities field in the same order, for example 0.2, 0.5, 0.3. -
Calculate
Click Calculate to fill the Mean, Variance and Std. Dev. boxes. -
Read the summary
Read the expected value (mean) and the spread (variance and standard deviation) from the three result 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
- Probability Distribution 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.