What this answers

This calculator answers "how many pairs do I need to reliably detect a correlation of about this size?" using the target correlation you expect to find as a planning assumption, the same role an assumed effect size plays in a mean or proportion sample-size calculation.

How it is calculated

Both the target correlation and the null correlation are converted to the Fisher z scale, where a correlation's sampling behavior is close to normal, using the same transform this site's Correlation Confidence Interval Calculator uses. The required sample size is the squared sum of the alpha-based and power-based z critical values, divided by the squared difference between the transformed target and null correlations, plus 3, a small-sample correction built into the standard formula.

Worked example

For a target correlation of .3 against a null of 0, at 95% confidence and 80% power, this calculator requires 85 pairs, a widely cited benchmark figure matching Cohen's published sample-size tables for detecting a small-to-medium correlation.

Assumption audit

Calculated from your data: the Fisher z transform of both the target and null correlations, and the resulting required sample size.

Evidence to review: how confident you are in the assumed target correlation; smaller assumed correlations require dramatically larger samples, so an overly optimistic assumption is a common way studies end up underpowered.

You must verify: that your planned analysis is a Pearson correlation between two roughly linearly related numeric variables, not a rank-based or nonlinear association, which this formula does not directly cover.

What this result does not mean

This sample size guarantees the stated power only if the true correlation in your population is at least as large as your target assumption; correlation, once found, still does not establish causation regardless of how well-powered the study was to detect it.

Common mistakes

Assuming a target correlation based only on what you hope to find, rather than what similar published research has actually observed, is the most common way this calculator produces an underpowered study. A second mistake is forgetting the null value entirely: leaving it at 0 answers "can I detect any correlation at all," a different and usually easier question than "can I distinguish this correlation from some other specific value," which a nonzero null answers instead.

Limitations

This calculator assumes a bivariate normal relationship, matching the Pearson correlation model it plans for; if you expect a strongly nonlinear or rank-based relationship instead, this sample-size formula will not transfer accurately to that different analysis.