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 for correlation calculator works
n≈3+[(zα+zβ)/(atanh(ρ₁)−atanh(ρ₀))]².
The target correlation must reflect the smallest association worth detecting, not an optimistic pilot estimate.
Worked example
Sample Size for Correlation example
Detecting correlation 0.3 against zero with 80% power and alpha 0.05 needs about 85 complete pairs.
n≈3+[(zα+zβ)/(atanh(ρ₁)−atanh(ρ₀))]².
Supported inputs
Precision and limits
Model and design
Uses Fisher-z asymptotics for independent bivariate observations and does not protect against nonlinearity or influential points.
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 target correlation must reflect the smallest association worth detecting, not an optimistic pilot estimate.
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.
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