When to use this calculator
An assumed proportion near 50% gives the largest normal-approximation requirement at a fixed critical value and margin.
Explore the sampling uncertainty calculators for other questions in this topic. For a related calculation, use the Standard Error Calculator: Estimate the standard error of a sample mean.
PUTTING IT INTO PRACTICE
Sample Size for a Proportion: 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 |
|---|---|
| Chosen z critical value | 1.96 |
| Assumed proportion (%) | 50 |
| Target margin (percentage points) | 5 |
| Result | 385 observations |
- Check the input labels and enter the example values above.
- Apply the relationship: n = ceiling(z² × p(1−p)/margin²).
- The result is 385 observations, rounded for display.
How to interpret your result
Assumes independent simple sampling, a large population and a normal approximation.
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 sample size for a proportion calculator useful?
An assumed proportion near 50% gives the largest normal-approximation requirement at a fixed critical value and margin.
How do I use the sample size for a proportion calculator?
Enter chosen z critical value, assumed proportion (%), target margin (percentage points). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
n = ceiling(z² × p(1−p)/margin²).
What should I check before using the result?
Assumes independent simple sampling, a large population and a normal approximation.
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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