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Sample Proportion and Standard Error Calculator — result sheet
Calculate a sample proportion and its simple binomial standard error from successes and trials.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: p̂=x/n; standard error=√[p̂(1−p̂)/n].
The observed proportion and its plug-in binomial standard error are reported without silently turning them into an interval.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Successes — minimum 0; maximum 1000000000
- Trials — minimum 1; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Successes | 48 |
| Trials | 120 |
p̂ =0.4; standard error ≈0.04472.
Assumptions and limits
- Successes and trials are whole counts with successes no greater than trials.
- The simple independent Bernoulli standard-error approximation is used.
- Finite populations, weighting, continuity correction, interval choice, and causal interpretation 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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