Sample size calculator: formula and interpretation
Reviewed: August 18, 2026. Sources, review and corrections methodology
DIRECT ANSWER
For a proportion with a large population, 95% confidence, 5% margin of error and p=0.5, the base sample is 385. For a finite population, apply n=N·n₀/(N+n₀−1). This calculation does not replace sampling design, feasibility or eligibility criteria.
Sample size calculator
For estimating one proportion. Leave population empty for a large or unknown population.
ESTIMATED MINIMUM
292
usable responses; adjust separately for expected nonresponse.
The calculator on this page estimates sample size for a proportion. It is useful for descriptive surveys that estimate a percentage, but it does not automatically fit every study, hypothesis or statistical technique.
Inputs you must define
- Population (N): total number of eligible units. Treat it as large only when there truly is no known practical limit.
- Confidence level: the theoretical frequency with which intervals built in the same way would cover the parameter. 95% is common, not mandatory.
- Margin of error (e): desired absolute precision. A 5% error is 0.05 in the formula.
- Expected proportion (p): prior estimate of the percentage. Without prior information, 0.5 gives the most conservative size under this formula.
The initial large-population sample is:
n₀ = z² · p · (1 − p) / e²
For a finite population:
n = N · n₀ / (N + n₀ − 1)
Round the result upward because a fraction of a respondent cannot be sampled.
Example
For N=1,200, 95% confidence, 5% error and p=0.5, n₀ is approximately 384.15 and the finite correction yields about 291 participants. That value assumes a selection process compatible with the formula and usable responses.
Adjusting for nonresponse
If you expect 20% of invited participants not to respond, simply adding 20% is not exact. Divide the required sample by the expected response rate:
invitations = n / 0.80
For n=291, you would invite about 364 people. Document the assumption and how nonresponse will be recorded.
When not to use this calculator
- Comparing means or groups with statistical power requirements.
- Regression models with several predictors.
- Cluster sampling or complex designs without a design effect.
- Qualitative research, where selection is not based on a margin of error.
- Very small populations when a census is feasible.
- Clinical or experimental studies requiring an effect-specific calculation.
Sample size cannot repair an incomplete sampling frame, convenience selection or nonresponse bias. A large sample can still be unrepresentative.
What to report in the thesis
Explain the population, unit of analysis, sampling frame, eligibility criteria, formula, input values, result, rounding, nonresponse adjustment and selection process. Save a copy of the calculation and cite the methodological source required by your program.
If your study requires power, strata, clusters or several hypotheses, review research methodology guidance or data analysis. The Honduras thesis guide helps place this decision in the full process.
Primary and academic sources
These sources support the editorial review of this guide. Always verify the current rules of your own program.
- Introductory Statistics, OpenStax, Rice University
- Cochrane Handbook for Systematic Reviews, Cochrane
- R Manuals, The R Foundation
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