Correlation Coefficient Calculator

The correlation coefficient (r) is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where +1 indicates a perfect positive correlation, -1 a perfect negative correlation, and 0 means no linear correlation.

The Pearson correlation coefficient is the most widely used correlation measure. It assumes both variables are continuous and normally distributed. It calculates r by dividing the covariance of the two variables by the product of their standard deviations, giving a value between -1 and +1.

Enter comma-separated numeric values for your first variable in the Data Set X field and for your second variable in the Data Set Y field. Both datasets must contain the same number of values. The calculator instantly computes Pearson r, the means, standard deviations, and covariance.

To calculate Pearson r manually: (1) compute the mean of X and Y, (2) subtract each value from its mean to get deviations, (3) multiply paired deviations and sum them (this is the covariance numerator), (4) compute the sum of squared deviations for X and Y separately, (5) divide the sum of products by the square root of the product of the two sums of squares.

A correlation coefficient of 0.8 indicates a strong positive linear relationship between the two variables. As one variable increases, the other tends to increase as well. Generally, |r| > 0.7 is considered strong, 0.4–0.7 moderate, and below 0.4 weak.

Covariance measures the joint variability of two variables — positive covariance means they tend to move together, negative means they move oppositely. The correlation coefficient is simply the standardized form of covariance: it divides covariance by the product of the standard deviations, making the result unit-free and bounded between -1 and +1.

No. A high correlation coefficient shows that two variables are linearly related, but it does not prove that one causes the other. There may be confounding variables, reverse causation, or the relationship could be coincidental. Correlation is a starting point for investigation, not a proof of cause and effect.

You need at least 3 paired data points to compute a correlation coefficient, but results from very small samples are unreliable. Most statisticians recommend at least 10–30 paired observations for a meaningful r value, and more data generally leads to a more stable estimate.