What is the correlation coefficient?

The correlation coefficient (often Pearson's r) measures the strength and direction of the linear relationship between two quantitative variables. It ranges from -1 to +1.

How do I calculate Pearson’s r?

Subtract the mean from each value, multiply paired deviations, sum them up, and divide by the product of the standard deviations. This calculator does these steps for you.

How do I interpret r?

Values near +1 mean a strong positive linear relationship, values near -1 indicate a strong negative relationship, and values near 0 mean little to no linear relationship.

Correlation Coefficient Calculator (Pearson’s r)

Enter your data

Separate values with comma, space, semicolon, or line break. X and Y must have the same length.

X values variable X

Y values variable Y

Decimal places

Results

Pearson r

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r² (explained)

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n (pairs)

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Direction

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Least-squares regression line (Y on X)

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Interpretation: for every 1-unit increase in X, Y changes by the slope.

Correlation coefficient formula

This calculator uses the sample Pearson correlation coefficient:

r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √( Σ(xᵢ − x̄)² · Σ(yᵢ − ȳ)² )

where:

xᵢ, yᵢ are paired observations
x̄ is the mean of X and ȳ is the mean of Y
r ranges from −1 to +1

How to interpret r

This is a common guideline (not a strict rule):

|r| < 0.3 → weak / negligible linear relationship
0.3 ≤ |r| < 0.5 → moderate linear relationship
|r| ≥ 0.5 → strong linear relationship

Keep in mind: correlation ≠ causation. A high r does not prove that X causes Y.