Worked example: Sample Size Calculator
95%, 5% margin. This fixed reference example shows one complete scenario; the interactive results above use your current inputs.
View the example inputs
- Confidence
- 95%
- Margin of error
- 5 percentage points
- Expected proportion
- 50 %
- Population (0 = unlimited)
- 0
| Calculated quantity | Example result |
|---|---|
| Required completed responses | 385 |
Understanding data summaries and statistical uncertainty
Check the data before the summary
A mean summarizes total magnitude per observation, while a median locates the middle of an ordered data set. A few extreme values can affect them differently. Standard deviation describes spread in the original units; variance uses squared units. A frequency chart helps show distribution shape that one summary cannot capture.
Keep sample and population formulas distinct. A sample-variance calculation typically uses n−1 in its denominator. Repeated observations and units must be handled consistently, and a list of numbers does not by itself establish independent random sampling.
Choose the assumptions before reading the result
Confidence intervals, sample sizes and p-values depend on a specified model, confidence or tail convention, and data assumptions. A narrow calculated interval is not evidence that the assumptions were met. A p-value is not the probability that a hypothesis is true.
Use the page’s formula and worked example to check whether the statistic, sample size and degrees of freedom match the intended analysis. Do not substitute a population standard deviation for a sample value, or a one-sided test for a two-sided one, without changing the model.
Formula and calculation method
n₀=z²p(1−p)/e²; n=n₀/[1+(n₀−1)/N] for a finite population. Round upward. Simple random sampling is assumed; design effects and nonresponse are excluded.
Reference Sources
Frequently asked questions
How does this calculator work?
n₀=z²p(1−p)/e²; n=n₀/[1+(n₀−1)/N] for a finite population. Round upward. Simple random sampling is assumed; design effects and nonresponse are excluded.
What assumptions should I check?
Check the units and definitions shown beside each input. Results use the values you enter.
Can I save or print this calculation?
Use Copy link with inputs to reproduce the scenario, Download results for a text record, or Print. Where a schedule is shown, its CSV download includes every row.