Sample Size Calculator
Estimate how many participants or observations your study may need based on its primary objective, desired precision, statistical power, and expected data loss.
Plan your research sample
Choose a calculation and enter the assumptions for your primary analysis.
Your estimate will appear here
Select a study type, review the assumptions, and calculate the required sample.
Plan around the primary research objective
Sample size is not determined by the population alone.
A defensible calculation starts with the study's primary outcome and intended analysis. A descriptive survey needs a precision-based calculation, while a hypothesis test usually needs an effect size, significance level, and statistical power.
This calculator separates those objectives so researchers do not accidentally apply a survey formula to an experiment, correlation study, or group comparison.
Precision
Control how narrowly a mean or proportion should be estimated.
Power
Plan the probability of detecting the effect specified in advance.
Design
Account for independent groups, paired data, clusters, and allocation.
Data loss
Increase recruitment to protect the analyzable sample from attrition.
How to calculate a research sample
Document every decision so the calculation can be reproduced.
Define the primary outcome
Choose the single outcome and analysis that primarily determines the study size.
Specify the target
Set the required precision or smallest meaningful effect before collecting data.
Account for design
Consider allocation ratios, clustering, repeated observations, and finite populations.
Set recruitment
Round upward and inflate the analyzable requirement for expected attrition.
Inputs used in sample size planning
Each input represents a substantive or statistical decision.
| Input | Meaning | Effect on sample size |
|---|---|---|
| Confidence level | Long-run coverage targeted by a confidence-interval procedure. | Higher confidence requires a larger sample. |
| Margin of error | Maximum targeted half-width of a confidence interval. | Smaller margins require substantially larger samples. |
| Power | Probability of detecting the specified effect under the assumed model. | Higher power requires a larger sample. |
| Significance level | Planned Type I error threshold for the primary test. | A smaller alpha generally requires a larger sample. |
| Effect size | Smallest difference or association the study is designed to detect. | Smaller effects require larger samples. |
| Design effect | Variance inflation from clustering or complex sampling. | Values above 1 increase the required sample. |
| Attrition | Expected proportion of recruited cases that will not be analyzable. | Higher attrition increases the recruitment target. |
Common mistakes to avoid
- Do not use one universal formula. Surveys, experiments, correlations, and diagnostic studies require different planning methods.
- Do not choose an optimistic effect. Base the calculation on the smallest meaningful effect, not the largest effect previously reported.
- Do not forget clustering. Students within classes, patients within hospitals, and repeated observations are not automatically independent.
- Do not confuse analyzable and recruited samples. Attrition should be added after the analysis requirement is determined.
- Do not round downward. Required counts should always be rounded upward.
What to report in a methodology
A sample size justification should identify the primary analysis, formula or software, significance level, power or precision target, assumed effect or variability, allocation ratio, population correction, design effect, attrition allowance, and final recruitment target.
Explain where the assumptions came from. Suitable sources may include previous studies, a pilot dataset, validated benchmarks, or a clearly defined minimum meaningful effect.
Frequently asked questions
For estimating a population proportion, the required sample depends on the confidence level, margin of error, expected proportion, and population size. When no expected proportion is available, 50% is commonly used because it produces the most conservative sample size.
A 95% confidence level is common, but the appropriate level should follow the study protocol, discipline, and consequences of uncertainty. Higher confidence levels require larger samples when all other inputs remain unchanged.
The margin of error should reflect the precision needed for the research decision. A smaller margin of error requires a larger sample. Five percentage points is common for general surveys, but it is not universally appropriate.
When estimating a proportion and no prior estimate is available, 50% maximizes p multiplied by one minus p. This results in the largest and therefore most conservative sample size for a given confidence level and margin of error.
Apply it when sampling without replacement from a known finite population and the calculated sample is not negligible relative to that population. It reduces the required sample because the population contains limited units.
Power is the probability of detecting the specified effect when that effect truly exists under the assumptions of the analysis. A target of 80% is common, but higher power may be justified for important or confirmatory studies.
Use the smallest effect that would be substantively important, ideally supported by prior studies, pilot data, theory, or a clinically or educationally meaningful threshold. Choosing an effect only because it produces a convenient sample can underpower the study.
Design effect represents the increase in variance caused by a complex sampling design compared with simple random sampling. For cluster sampling it is often estimated as 1 plus the average cluster size minus one, multiplied by the intraclass correlation.
Divide the required analyzable sample by one minus the expected attrition proportion. For example, a required final sample of 100 with 20% expected attrition requires recruiting 125 participants.
No. The calculations use standard approximations and simplified assumptions. Multilevel designs, complex longitudinal models, survival analyses, equivalence or noninferiority studies, rare outcomes, multiple primary endpoints, and adaptive designs may require simulation or specialist software.
Always round upward. For equal-group studies, round the per-group requirement upward and recruit enough participants to preserve the planned allocation ratio.
A design-specific calculation based on the primary outcome, target effect, significance level, power, and expected data loss is generally more defensible than a broad rule of thumb. Clearly report every assumption used.