Pearson Correlation
Calculate Pearson’s r from -1 to +1 and identify whether the variables move together or in opposite directions.
Statistical Analysis Tool
Correlation Coefficient Calculator
Calculate the Pearson correlation coefficient between two datasets and instantly understand the direction, strength, covariance, and shared variation of the relationship.
Enter Your Paired Data
Use commas, spaces, semicolons, or new lines.
Calculated in your browser
Calculator features
More Than a Basic Correlation Result
Get the statistical values needed to evaluate the strength and direction of a linear relationship.
R-Squared Value
See the coefficient of determination and the percentage of variation shared by the two datasets.
Covariance Analysis
Review sample covariance, dataset means, paired values, and a clear interpretation of your result.
Simple process
How the Correlation Calculator Works
Calculate and interpret a correlation coefficient in three straightforward steps.
1
Enter Dataset X
Add the values for your first variable using commas, spaces, semicolons, or separate lines.
2
Enter Dataset Y
Add the corresponding values for the second variable. Both datasets must have equal lengths.
3
Review the Analysis
Select calculate to view Pearson’s r, R-squared, covariance, means, and relationship strength.
What Is a Correlation Coefficient?
A correlation coefficient is a statistical measurement that describes the direction and strength of a relationship between two variables. The Pearson correlation coefficient, represented by the letter r, is commonly used to measure linear relationships.
The result always falls between -1 and +1. A positive result indicates that the variables generally increase together. A negative result indicates that one variable tends to decrease as the other increases. A result near zero indicates little or no linear relationship.
Pearson Correlation Coefficient Formula
r = Σ[(x − x̄)(y − ȳ)] ÷ √[Σ(x − x̄)² × Σ(y − ȳ)²]
In this formula, x̄ is the mean of Dataset X and ȳ is the mean of Dataset Y. The calculation compares how each paired observation differs from its dataset mean.
How to Interpret Correlation Strength
The absolute value of the coefficient indicates the relationship’s strength, while its positive or negative sign indicates direction. Interpretation can vary by field, but the following guidelines are commonly used.
| Absolute r value | Relationship strength | General meaning |
|---|---|---|
| 0.00 to 0.19 | Very weak | Little or no linear relationship |
| 0.20 to 0.39 | Weak | A small linear association |
| 0.40 to 0.59 | Moderate | A noticeable linear association |
| 0.60 to 0.79 | Strong | A substantial linear association |
| 0.80 to 1.00 | Very strong | A highly consistent linear association |
What Does R-Squared Mean?
R-squared is calculated by squaring the correlation coefficient. It represents the proportion of variation in one variable that is linearly associated with variation in the other variable. For example, an r value of 0.80 produces an R-squared value of 0.64, or 64 percent shared variation.
Correlation Does Not Prove Causation
A strong correlation does not prove that one variable causes changes in another. The relationship may be influenced by coincidence, hidden variables, sampling choices, or another external factor. Correlation results should therefore be interpreted alongside subject knowledge and an appropriate research design.
Common questions
Correlation Coefficient Calculator FAQs
Helpful answers about calculating and interpreting Pearson correlation.
A “good” correlation depends on the research field and purpose. An absolute r value above 0.70 is often considered strong, but lower values may still be meaningful in complex fields such as social science.
A coefficient of -1 represents a perfect negative linear correlation. As one variable increases, the other decreases in a perfectly consistent pattern.
A coefficient of zero means no linear relationship was detected. The variables may still have a nonlinear relationship that Pearson’s r does not capture.
Yes. Correlation is calculated from paired observations, so every X value must have one corresponding Y value.
The calculator requires at least two valid pairs, although a larger and representative sample generally provides a more reliable result.
No. The statistical calculation is performed directly in your browser using JavaScript. Your entered datasets are not uploaded by this tool.