researchtools
Statistics

Pearson Correlation Calculator

Calculate Pearson r, two-sided p-value and linear trend.

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ABOUT THIS TOOL

Calculate Pearson’s product-moment correlation coefficient and a two-sided t-based p-value from paired numerical observations.

Important: Pearson r summarizes linear association. The t-based p-value assumes independent paired observations and bivariate normality under the null. Review outliers, nonlinearity and sampling dependence; association is not causation.

How it works

Method: Pearson r = Σ[(x − x̄)(y − ȳ)] / √[Σ(x − x̄)² × Σ(y − ȳ)²]. The two-sided t-test uses t = r × √[(n − 2)/(1 − r²)] and n − 2 degrees of freedom under its assumptions.

Example: For the exact linear pairs (1,2), (2,4), (3,6), Pearson r = 1. Inspect the scatter plot, and do not confuse correlation with causation.

Cite this toolCopy · BibTeX · RIS

If you use this calculator in research, you may cite the software and report the statistical methods separately. Citation is appreciated, not required. No DOI is registered for this release.

Biotech Insight Solutions. ResearchTools: Pearson Correlation Calculator (version 1.4) [Software]. 2026. Available at: https://tools.biotech-insight.com/tools/pearson-correlation/

A citation cannot replace a methods description or independent verification. Report version, statistical assumptions and data-processing choices.

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