Pearson Correlation Coefficient Calculator

Formula first

Overview

The Pearson product-moment correlation coefficient (r) quantifies the degree to which two continuous variables are linearly related. Its value ranges from -1 to +1, where +1 indicates a perfect positive linear relationship, -1 a perfect negative linear relationship, and 0 no linear relationship.

Symbols

Variables

r = Pearson Correlation Coefficient, $x_i$ = Individual x value, $y_i$ = Individual y value, $\bar{x}$ = Mean of x, $\bar{y}$ = Mean of y

Apply it well

When To Use

When to use: Use this formula when examining the linear association between two continuous variables and you need a single standardized measure of how strongly they move together.

Why it matters: It is a core statistic in data analysis, social science, and machine learning because it summarizes both direction and strength on a fixed scale from -1 to 1.

Avoid these traps

Common Mistakes

• Confusing correlation with causation.
• Using Pearson's r on a clearly non-linear relationship.
• Ignoring outliers or mismatching paired observations.

One free problem

Practice Problem

A dataset has x = [1, 2, 3] and y = [2, 4, 6]. Calculate the Pearson correlation coefficient.

Solve for: $r$

Hint: A perfectly straight upward line gives r = 1.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Britannica Editors (2026) 'Correlation coefficient' Encyclopaedia Britannica.
2. NIST/SEMATECH e-Handbook of Statistical Methods, correlation and regression sections.
3. NIST Special Publication 500-339, correlation matrix and regression statistics.
4. Understanding the Pearson Correlation Coefficient | Outlier
5. Pearson correlation coefficient - Wikipedia
6. What is an intuitive explanation of the Pearson product-moment correlation coefficient?
7. Pearson correlation coefficient (PCC) | Science | Research Starters - EBSCO
8. Pearson Correlation Coefficient (r) | Guide & Examples - Scribbr