Estimate how many survey responses you need from a population using confidence level, margin of error, and expected proportion, with the finite population correction shown step by step.
For a population of 10,000, 95% confidence, 5% margin of error, and 50% expected proportion, the recommended sample size is about 370 completed responses.
Enter survey assumptions to calculate responses.
How to use the sample size calculator
Enter the total population size, choose a confidence level, set your acceptable margin of error, and enter the expected proportion. The calculator first finds the large-population sample size, then applies the finite population correction when the population is known.
A 50% expected proportion produces the largest required sample size, so it is a cautious default for many surveys.
Survey planning normally rounds the final sample size upward because a partial respondent cannot complete a survey.
Sample size formula
n₀ = z²p(1−p) ÷ e² gives the initial sample size for a proportion. When the population size N is known, the adjusted sample size is n = n₀ ÷ [1 + (n₀ − 1) ÷ N].
Worked example
For N = 10,000, 95% confidence, 5% margin of error, and p = 0.50, z = 1.96. The initial sample size is about 384.16. After finite population adjustment, the result is about 369.98, so the survey should target at least 370 completed responses.
Planning notes for real surveys
| Decision | Effect |
|---|---|
| Higher confidence | Needs a larger sample. |
| Smaller margin of error | Needs a larger sample. |
| Unknown proportion | Use 50% for a conservative estimate. |
| Low response rate | Invite more people than the final sample size. |
Common mistakes
- Using invited participants instead of completed responses as the sample size.
- Forgetting to round the final result up.
- Choosing a very small margin of error without enough budget or time.
- Using this proportion formula for every statistical design without checking the assignment or study method.
- Ignoring nonresponse, sampling bias, or the way respondents are selected.
Sample size calculator FAQs
What confidence level should I use?
Many school, market research, and survey examples use 95%. A 99% level is stricter and requires more responses. A 90% level is less strict and requires fewer responses.
What margin of error should I choose?
Five percent is common for general surveys. Smaller margins, such as 3%, need more responses and are harder to achieve.
Why does 50% proportion give the largest sample size?
The term p(1−p) is largest when p = 0.50. That makes the estimate conservative when the true proportion is unknown.
Does this guarantee a representative sample?
No. The formula estimates quantity, not quality. Your sample method must still avoid bias and reach the right population.
Can I use this for a mean instead of a proportion?
This page is built for proportion-style survey planning. For mean-based intervals, use a confidence interval calculator with standard deviation and sample size.
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Reviewer
This educational math content is reviewed under the SolverCalc reviewer rule by Prof. Dr. Khalil Mudassar. WordPress adds the author bio automatically, so this page does not include a duplicate author box.
Plan the next step
After estimating sample size, use confidence intervals, standard deviation, and related statistics tools to interpret the results responsibly.
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