Correlation Coefficient Calculator

The correlation coefficient measures how strongly two variables move together, on a scale from −1 to +1. A value near +1 means they rise together, near −1 means one falls as the other rises, and near 0 means there is little linear relationship. This correlation coefficient calculator returns Pearson’s r along with R-squared so you can judge both the direction and the strength of the link between your paired x and y values.

How to use this calculator

1. Enter your x values in the first box, separated by commas, spaces, or new lines (for example, 1, 2, 3, 4, 5).
2. Enter the matching y values in the second box, in the same order, so each x pairs with its own y.
3. Read the correlation coefficient (r) for the strength and direction of the relationship, and R-squared for the share of variation in y that the straight-line fit explains.

Both lists must have the same length and at least two paired values, and each variable needs some spread — a column of identical numbers has no variation to correlate.

Worked example

Take five paired values: x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 5.

First find the sums of squares around each mean (x̄ = 3, ȳ = 4):

Sxx = Σ(xi − x̄)² = 10
Syy = Σ(yi − ȳ)² = 6
Sxy = Σ(xi − x̄)(yi − ȳ) = 6

Then divide the cross-product term by the square root of the other two:

r = Sxy / √(Sxx × Syy) = 6 / √(10 × 6) = 6 / √60 ≈ 0.7746
R² = r² ≈ 0.60

So r ≈ 0.77 is a fairly strong positive correlation, and the linear fit explains about 60% of the variation in y. For the formal definition of Pearson’s product- moment coefficient, see the NIST/SEMATECH e-Handbook on linear correlation.

Frequently asked questions

What does the r value actually tell you?

The r value reports the direction and strength of a linear relationship. The sign shows direction (+ together, − opposite) and the size shows strength: roughly 0.1–0.3 is weak, 0.3–0.5 moderate, and above 0.5 strong, though the thresholds depend on your field.

How is the Pearson correlation different from R-squared?

Pearson correlation (r) ranges from −1 to +1 and keeps the sign. R-squared is simply r multiplied by itself, so it ranges from 0 to 1 and tells you the proportion of variance in y explained by x — but it drops the direction.

Does a high correlation mean one variable causes the other?

No. A strong correlation only shows that two variables move together; it cannot prove that one causes the other, because a hidden third factor or coincidence can produce the same pattern.