Pearson Correlation Coefficient Calculator

Calculate Pearson r, r squared, covariance, and correlation strength from paired x,y data with a scatter plot and step-by-step table.

Pearson r r squared Scatter Plot
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Paired data

Enter one pair per line. Commas and spaces both work.

Input guide

Accepted formats

1,2
1 2
-3.5, 4e2

Pearson r scale

-1 is perfect negative, 0 is no linear correlation, and +1 is perfect positive.

Important

Correlation measures association. It does not prove causation.

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Calculating correlation...

Submit paired data to calculate Pearson r

The result will show r, r squared, covariance, a scatter plot, and a step-by-step deviation table.

Positive linear association r ≈ 0.99

Pearson r explained

What the correlation coefficient measures

The Pearson correlation coefficient calculator measures the strength and direction of a linear relationship between two numeric variables. Pearson r ranges from -1 to +1: negative values slope downward, positive values slope upward, and values near 0 show little linear association.

The r squared value is r multiplied by itself. It describes the share of variation aligned with the fitted linear relationship in the submitted data, but correlation does not prove causation.

Pearson r formula

Pearson r compares centered x and y movement against their total squared spread.

r = Sxy / sqrt(Sxx x Syy) Sxy shared movement Sxx x spread Syy y spread

Correlation scale

The sign gives direction; the distance from 0 gives strength.

-1 0 +1 negative none positive

Scatter plot patterns

Pearson r is easiest to understand visually: points close to a line produce stronger absolute correlation.

Positive

r > 0

Negative

r < 0

Weak / none

r near 0

Example correlation values

r valueDirectionMeaning
0.95PositiveNear-perfect upward linear association
-0.82NegativeVery strong downward linear association
0.28PositiveWeak upward linear association
0.02Near zeroLittle or no linear association

FAQ

What is Pearson r?

Pearson r is a number from -1 to +1 that describes the direction and strength of a linear relationship between two numeric variables.

What is r squared?

R squared is r multiplied by itself. It is often read as the share of variation aligned with a linear relationship in the data.

Does correlation prove causation?

No. Pearson correlation can identify association, but study design and domain evidence are needed before making causal claims.