Pearson Correlation Calculator
Calculate Pearson's correlation coefficient to measure the strength and direction of the linear relationship between two sets of paired data. Get r, R², sample size, t-statistic, p-value, and an easy-to-understand interpretation instantly.
Enter Paired Data
Enter the same number of X and Y values.
What Is Pearson Correlation?
Pearson correlation is a statistical measure used to describe the strength and direction of a linear relationship between two numeric variables. The result is known as Pearson's correlation coefficient and is represented by the letter r.
The value of r always falls between −1 and +1. A value close to +1 represents a strong positive linear relationship, while a value close to −1 represents a strong negative linear relationship. Values around zero indicate little or no linear correlation.
What Does a Positive Correlation Mean?
A positive correlation means the two variables generally move in the same direction. As X increases, Y also tends to increase.
What Does a Negative Correlation Mean?
A negative correlation means the variables generally move in opposite directions. As one variable increases, the other tends to decrease.
How to Use the Pearson Correlation Calculator
Enter X Values
Add the observations for your first variable in the X Values field. Separate each number with a comma, space, or new line.
Enter Y Values
Enter the corresponding observations for your second variable. The number of X and Y observations must match.
Calculate Pearson r
Click Calculate Correlation to instantly see r, R², sample size, t-statistic, p-value, direction, and correlation strength.
How to Interpret Pearson's Correlation Coefficient
The absolute size of Pearson's r describes the strength of the linear relationship, while its positive or negative sign shows the direction. The following ranges provide a convenient general guide, although interpretation may vary by field and context.
| Absolute r Value | Correlation Strength | Meaning |
|---|---|---|
| 0.00 – 0.19 | Very Weak | Little linear association |
| 0.20 – 0.39 | Weak | Small linear association |
| 0.40 – 0.59 | Moderate | Noticeable linear association |
| 0.60 – 0.79 | Strong | Clear linear association |
| 0.80 – 1.00 | Very Strong | Very close linear association |
What Is R-Squared in Correlation?
R-squared is calculated by squaring Pearson's correlation coefficient. In a simple linear relationship between two variables, R² provides a measure of the proportion of variance associated with their linear relationship.
For example, if r = 0.80, then R² = 0.64. This should be interpreted carefully and within the context of the data, especially because correlation alone does not establish a causal relationship.
Pearson Correlation Significance Test
When there are at least three paired observations and |r| is less than 1, a t-statistic can be calculated from the correlation coefficient. The degrees of freedom equal n − 2, where n is the number of paired observations.
Pearson Correlation Example
Suppose you are comparing hours studied with exam scores. Study hours could be entered as X values and corresponding exam scores as Y values. If students who study for more hours generally achieve higher scores, the calculator may return a positive Pearson correlation.
An r value close to +1 would indicate that the observations are closely aligned with an upward-sloping straight-line pattern. A smaller positive value would indicate that the upward relationship exists but is less consistent.