What this calculator estimates
This calculator estimates sample size for a simple random sample when the main outcome is a proportion, such as the percentage of respondents who choose an option. It uses a normal-approximation planning formula and rounds up because partial respondents are not possible.
Example
For a 95% confidence level, 5% margin of error and expected proportion of 50%, the simple planning formula gives about 385 responses before any finite population adjustment. Tightening the margin to 3% requires far more responses.
Inputs that matter most
- Margin of error: smaller margins require much larger samples.
- Confidence level: higher confidence increases the z value and sample size.
- Expected proportion: 50% is conservative when the true proportion is unknown.
- Population size: only reduces the estimate when the total population is known and not very large.
Limitations
The formula assumes a simple random sample. It does not adjust for design effects, quotas, weighting, nonresponse, panel quality, cluster sampling or measurement bias. For formal research, treat this as a planning estimate and document the actual sampling method.
References
- NIST/SEMATECH e-Handbook: Confidence intervals - confidence interval basis for sample-size planning, accessed 2026-05-17.
FAQ
What proportion should I use if I do not know it?
A planning value of 50% is conservative for a simple proportion because it usually produces the largest required sample size.
Does this replace survey design?
No. Sampling method, nonresponse, weighting, clustering and data quality can matter more than the simple formula.
Why does finite population size reduce the sample?
When the population is small and known, the finite population correction adjusts the simple random sample estimate downward.
Last reviewed: 2026-05-17