Planning balances the effect worth detecting, sample size, false-positive rate, and target power.
80% target powerα = 0.05
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Statistics result
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Sample Size. Planning starts with an effect worth detecting, a significance level, a target power, and assumptions about variation or baseline rates.
1Define the smallest meaningful effect2Set alpha, power, and allocation3Round sample requirements upward and allow for attrition
Method used
n₀=z²p(1−p)/E²; n=n₀/[1+(n₀−1)/N].
The result addresses sampling precision, not nonresponse, bias, clustering, exclusions, or measurement error.
What the result cannot establish
Power is a long-run probability under the assumed effect and model. It is not a guarantee of significance, data quality, or practical importance.
Assumption: The normal approximation and a simple random sample are assumed; use p=0.5 when no planning estimate is defensible.
Quick guide
How to use this calculator
Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the sample size calculator works
n₀=z²p(1−p)/E²; n=n₀/[1+(n₀−1)/N].
The result addresses sampling precision, not nonresponse, bias, clustering, exclusions, or measurement error.
Worked example
Sample Size example
At 95% confidence, 5% margin, and p=0.5, the uncorrected minimum is 385.
n₀=z²p(1−p)/E²; n=n₀/[1+(n₀−1)/N].
Supported inputs
Precision and limits
Model and design
The normal approximation and a simple random sample are assumed; use p=0.5 when no planning estimate is defensible.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The result addresses sampling precision, not nonresponse, bias, clustering, exclusions, or measurement error.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
