Correlation Calculator

Measure the strength and direction of a linear relationship.

How Pearson correlation works

Pearson's correlation coefficient r measures the strength and direction of a linear relationship between two variables, from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive).

The calculator requires paired X and Y values of equal length, at least two pairs, and at least one variable must vary (a constant column has zero variance and no defined correlation).

Correlation describes association, not causation: two variables can be strongly correlated without one causing the other.

The formula

r = Σ((x−x̄)(y−ȳ)) ÷ √(Σ(x−x̄)² · Σ(y−ȳ)²)

For each pair, multiply the deviations of x and y from their means, sum them, and divide by the square root of the product of the summed squared deviations of x and y.

Worked example

Perfect positive relationship

For X = 1,2,3,4,5 and Y = 2,4,6,8,10 every point lies exactly on a rising line, so r = 1. If Y were 10,8,6,4,2, r would be −1.

Frequently asked questions

How do I interpret the strength of r?

As a rough guide, |r| below 0.3 is weak, 0.3–0.7 is moderate, and above 0.7 is strong. Context and sample size matter — always consider both.

Why do I get an error for constant data?

If all X values are identical there is no variance in X, so the correlation is undefined. Add a dataset with some variation.

Does correlation imply causation?

No. Correlation alone cannot establish cause and effect — a third variable may drive both, or the relationship may be coincidental.

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