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Input two sets of continuous data, quickly calculate Pearson correlation coefficient R, and determine the strength of linear correlation.
The number of data points for X and Y must be equal and correspond one-to-one. Each set requires at least 2 numbers (at least 3 for significance testing). Supports separation by commas, spaces, newlines, or semicolons. Non-numeric content will be ignored.
Enter paired X and Y data to view the correlation coefficient.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Enter paired numeric observations in X and Y lists. The first X value pairs with the first Y value, the second with the second, and so on. Pearson’s sample correlation coefficient, r, ranges from −1 to +1: its sign indicates direction, while its magnitude describes how closely points follow a straight-line pattern. A value near zero means little linear association in the sample; it does not rule out a curved relationship.
r = Sxy / √(Sxx · Syy)
Sxy = Σ(xi − meanX)(yi − meanY); Sxx and Syy are sums of squared deviations.
Results also include the pair count, means, sample standard deviations, sample covariance, R² = r², and a least-squares line y = slope × x + intercept. The line describes the fitted linear relationship in the sample; it is not a causal model.
You can enter a significance level α between 0 and 1; the initial value is 0.05. With more than two pairs and a computed correlation other than exactly ±1, the page calculates a t statistic with n − 2 degrees of freedom and a two-sided p-value for the null hypothesis that population correlation is zero. If α is blank or invalid, the calculation uses 0.05. The result compares p with α and reports whether the null is rejected at that threshold.
A p-value depends on the statistical model and data assumptions; it is not the probability that the null is true or a measure of practical importance. Review the paired observations and scatter plot for curvature, clusters, and influential outliers.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Keep X and Y in the same order so each position describes the same case or subject. Separate numbers with commas, spaces, semicolons, tabs, or line breaks.
At least two valid values are required in each list, and the valid counts must match. Non-numeric tokens are ignored, so remove labels and stray text rather than treating them as missing-value placeholders.
Use a value strictly between 0 and 1. A blank or invalid value falls back to 0.05. The significance test is available only when the sample permits it.
Compare r, the fitted line, and the scatter plot. The displayed calculation steps show intermediate quantities used for the coefficient.
Use cases
See how the tool fits into real work and everyday tasks.
An analyst with matched measurements can use r and the scatter plot as an exploratory summary before choosing a fuller model.
A student can compare means, sums of deviations, the coefficient, and test output to understand the contents of a paired-data correlation calculation.
Q&A
Find concise answers to common questions and confusing cases.
Yes. Pearson’s r measures linear association. A curved pattern can have a small r, so inspect the scatter plot.
The test is not shown with only two pairs or when r is exactly +1 or −1. The coefficient and related sample statistics may still be available.
Only tokens that parse as finite numbers are used. Text labels and invalid numeric strings are skipped, which can change the number of pairs.
No. Correlation describes association in the sample. A small p-value does not establish causation, rule out confounding, or show practical importance.
Notes
Review scope, result limitations, and important precautions before use.
Each pair should be a meaningful matched observation, and observations should be collected in a way that supports your inference. The conventional t test for zero population correlation relies on assumptions about the sampling distribution, including independent observations and a suitable bivariate model. Extreme outliers can strongly affect Pearson’s coefficient and the fitted line. Use subject context, a plot, and an appropriate statistical method before drawing formal conclusions. Correlation alone cannot establish cause and effect.
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