When to use this calculator
This measures sampling uncertainty of an estimated share, rather than variation among individual binary observations.
Explore the sampling uncertainty calculators for other questions in this topic. For a related calculation, use the Sample Size for a Proportion Calculator: Estimate a normal-approximation sample size for a target proportion margin.
PUTTING IT INTO PRACTICE
Proportion Standard Error: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Sample proportion (%) | 50 |
| Sample size (integer) | 100 |
| Result | 5 percentage points |
- Check the input labels and enter the example values above.
- Apply the relationship: Standard error in percentage points = √(p(1−p)/n) × 100.
- The result is 5 percentage points, rounded for display.
How to interpret your result
This plug-in estimate does not correct for clustering, small samples or boundary proportions.
Use a critical value and model appropriate to the study. Simple random-sampling approximations do not correct for selection bias or clustered observations. Normal approximations can be poor for small samples or extreme proportions.
Frequently asked questions
Does a larger sample remove selection bias?
No. More observations can reduce sampling variability without repairing a systematically biased selection process.
When is the proportion standard error calculator useful?
This measures sampling uncertainty of an estimated share, rather than variation among individual binary observations.
How do I use the proportion standard error calculator?
Enter sample proportion (%), sample size (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Standard error in percentage points = √(p(1−p)/n) × 100.
What should I check before using the result?
This plug-in estimate does not correct for clustering, small samples or boundary proportions.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST/SEMATECH statistical methods handbook ↗. This is a topic reference, not an external review or endorsement of this tool.
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