Correlation Meta-Analysis Calculator

Combine correlations from independent studies

Use this correlation meta-analysis calculator to pool Pearson correlation coefficients. Enter each study's r and sample size in the table above. The calculator combines the correlations using Fisher's z transformation and reports the pooled result and its 95% confidence interval as correlation r.

Select Correlations under Study data. You need summary results from at least two independent studies. To calculate a correlation from individual participants' paired observations, use the correlation calculator instead.

How to calculate a pooled correlation

1. Select Correlations, then enter an optional study label, Pearson's r, and the number of paired observations used to calculate that r.
2. Enter, paste or import one row per independent study in the table above, then select the correlation, sample-size and optional study-label columns. Enter r as a decimal, such as 0.32, rather than as 32%.
3. Choose a fixed-effect or random-effects model based on the research question and study designs. For random effects, use the Estimator and Hartung–Knapp adjustment controls; the defaults are REML with the adjustment on.
4. Read the combined r and its 95% confidence interval in Pooled results. Check the forest plot, study weights, and heterogeneity below it.

How is the combined correlation calculated?

Each correlation is transformed using z = 0.5 * ln((1 + r) / (1 - r)), with sampling variance v = 1 / (n - 3). Fixed-effect weights are 1 / v; random-effects weights are 1 / (v + tau-squared), where tau-squared is estimated by REML (the default) or DerSimonian-Laird. Fixed-effect confidence intervals use a normal approximation. For random effects, Hartung-Knapp adjusts the pooled standard error and uses a t distribution with k - 1 degrees of freedom, where k is the number of studies; turning it off gives normal-approximation intervals. The weighted mean z, its 95% confidence limits, and the random-effects 95% prediction limits are transformed back using r = tanh(z).

The combined r is therefore not a simple arithmetic average of the entered correlations. The forest plot and study results are displayed as r, while heterogeneity calculations and the funnel plot use Fisher's z. Tau-squared is a variance on the Fisher's z scale, not on the original r scale.

Check these inputs before pooling

• Each r must be strictly between -1 and 1. Sample sizes must be whole numbers greater than three.
• Use the sample size for the reported correlation, which may be smaller than the study's total recruitment if observations are missing.
• Keep the same construct definitions and scoring directions. Reverse coding can change the sign of a correlation.
• Use independent estimates. Multiple correlations from the same participants, overlapping samples, or repeated measurements require methods that account for dependence.
• This input format is for Pearson correlations. It does not provide specialized sampling-variance calculations for Spearman, Kendall, partial, or reliability-corrected correlations.

Read and keep your results

A positive pooled r indicates an association in the same direction; a negative r indicates an inverse association, given consistent coding. An interval containing zero includes no linear association. Correlation does not establish causation, and practical importance depends on the research context.

For random effects, the 95% prediction interval estimates the range for the true correlation in a new, comparable study. It assumes normally distributed true effects on the Fisher's z scale and can be unreliable with few studies; it is not the confidence interval of the pooled r.

Use the heterogeneity results to assess inconsistency and the forest plot to inspect individual estimates. Use the table filter to exclude a study without deleting its data. Use export / import above the table to save or reopen your input data. Report the model, estimator, Hartung-Knapp setting, number of studies, pooled r, confidence interval, any prediction interval, and heterogeneity with the analysis scale.

For background on Pearson's r, see the Pearson correlation tutorial. The metafor effect-size documentation describes Fisher's z-transformed correlations and sampling variances.