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Binomial Mean and Variance Calculator — result sheet
Calculate the expected successes, variance, and standard deviation for a binomial model.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: E(X)=np; Var(X)=np(1−p); SD=√(np(1−p)).
The three outputs summarize the center and spread of a count of successes under identical independent trials.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of trials n — minimum 1; maximum 1000000000
- Success probability p — %; minimum 0; maximum 1
Worked example
| Input | Value |
|---|---|
| Number of trials n | 20 |
| Success probability p | 0.4 |
Expected successes =8; variance =4.8; standard deviation ≈2.191.
Assumptions and limits
- The number of trials is a positive whole number and p is between zero and one.
- Trials are independent with a common success probability.
- Dependence, changing probabilities, and a full probability table are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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