Correlation Coefficient Calculator
Measure the strength and direction of the linear relationship between two variables with Pearson’s r, along with R², covariance, and a scatter plot.
- R² (determination)
- 0.9318
- Covariance
- 5.5000
- n (pairs)
- 8
- Slope
- 0.9167
Scatter plot
r = 0.9653What is the correlation coefficient?
Pearson’s correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from −1 to +1: values near +1 indicate a strong positive relationship, values near −1 a strong negative relationship, and values near 0 little or no linear relationship.
Correlation formula
Pearson’s r is the covariance of x and y divided by the product of their standard deviations:
How to interpret r
| |r| | Strength |
|---|---|
| 0.0 – 0.3 | Weak |
| 0.3 – 0.7 | Moderate |
| 0.7 – 0.9 | Strong |
| 0.9 – 1.0 | Very strong |
Correlation in Excel
Use =CORREL(x_range, y_range) or =PEARSON(x_range, y_range) to get the correlation coefficient. =RSQ(y_range, x_range) gives R².
Frequently asked questions
What is the difference between r and R²?
r is the correlation coefficient, ranging from −1 to 1, showing strength and direction. R² is r squared, ranging from 0 to 1, and gives the proportion of variance in one variable explained by the other.
What does a negative correlation mean?
A negative correlation means that as one variable increases, the other tends to decrease. The closer r is to −1, the stronger that inverse relationship.
Does correlation mean causation?
No. A strong correlation shows two variables move together, but it does not prove that one causes the other — a third factor or coincidence may explain the pattern.