Use this free Pearson product-moment correlation calculator to measure the strength and direction of a linear relationship between two numeric variables. Paste your paired data below, click calculate, and instantly get the correlation coefficient (r) plus an easy interpretation.
Pearson Correlation Calculator
Enter two equal-length lists of numbers. You can separate values with commas, spaces, tabs, or new lines.
What Is the Pearson Product-Moment Correlation?
The Pearson product-moment correlation coefficient is one of the most common statistics in data analysis. It tells you how closely two variables move together in a straight-line pattern. The value of r is always between -1 and +1.
- r = +1: perfect positive linear relationship
- r = 0: no linear relationship
- r = -1: perfect negative linear relationship
If one variable increases while the other also tends to increase, the correlation is positive. If one increases while the other tends to decrease, it is negative.
How to Use This Calculator
Step-by-step input guide
- Put your first variable in the X values box.
- Put the matching second variable in the Y values box.
- Make sure both lists have the same number of observations.
- Click Calculate Correlation to get your result instantly.
Each X value must pair with a Y value from the same case, participant, or time point. Paired structure is essential for a valid result.
How to Interpret the Correlation Coefficient
Direction and magnitude
A positive sign means the variables trend together. A negative sign means they trend in opposite directions. The absolute size of r indicates how strong the linear relationship is.
- 0.00 to 0.09: negligible
- 0.10 to 0.29: weak
- 0.30 to 0.49: moderate
- 0.50 to 0.69: strong
- 0.70 to 0.89: very strong
- 0.90 to 1.00: nearly perfect
What r² tells you
Squaring r gives r², the coefficient of determination. It estimates how much variation in one variable is linearly associated with variation in the other. For example, if r = 0.80, then r² = 0.64, meaning about 64% shared linear variance.
Assumptions for Pearson Correlation
Before relying on Pearson r, check key assumptions:
- Both variables are numeric and measured on interval/ratio scales.
- The relationship is approximately linear (not strongly curved).
- Extreme outliers are limited because they can distort r.
- Observations are independent.
If your data are ordinal or clearly non-linear, a rank-based method like Spearman's rho may be more appropriate.
Example Use Cases
Education research
Evaluate whether hours studied are associated with exam scores.
Finance and economics
Explore whether marketing spend and sales revenue show a linear relationship.
Health analytics
Test whether physical activity levels correlate with resting heart rate.
Common Mistakes to Avoid
- Using unmatched X and Y lists (different lengths or wrong pairing order).
- Interpreting correlation as proof of causation.
- Ignoring outliers that can inflate or suppress r.
- Using Pearson r for strongly non-linear relationships.
Correlation is a powerful summary statistic, but always combine it with data visualization and domain context.