Pearson Correlation Coefficient Calculator

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Variable X (comma or space separated)

Variable Y (comma or space separated)

Calculate CorrelationClear

Enter paired numerical data

Enter one list for X and one for Y, with the same number of observations. Values can be separated by commas or whitespace. The first X belongs with the first Y, and so on.

Do not independently sort the columns or mix unmatched cases. Both variables need nonzero variation; correlation with a constant variable is undefined. The calculator’s significance test also needs at least three pairs.

This is a Pearson calculator. It does not calculate Spearman correlation, a regression line, or prediction intervals.

Reproduce a result

Enter X = 2,4,6,8,10 and Y = 65,75,80,88,92.

• Pearson r ≈ 0.9900.
• r² ≈ 0.9801.
• Under the classical independent-pair normal model, the two-sided zero-correlation p-value is approximately 0.0012.

The pairs are small hypothetical teaching data. Their tight fit is not evidence about a real student population. The correlation lesson shows the centered sums used in the calculation.

Interpret the coefficient

r measures linear association, with sign giving direction. It is unchanged by positive changes of measurement units, unlike a regression slope.

r = 0 does not imply independence or absence of every relationship. For X = −2, −1, 0, 1, 2 and Y = 4, 1, 0, 1, 4, the U-shaped pattern has r = 0.

For simple least-squares regression with an intercept, r² equals R². It describes the fitted line’s accounting for sample variation, not a causal percentage or guaranteed predictive accuracy on new data.

Interpret the p-value separately

The usual zero-correlation test uses t = r√(n − 2)/√(1 − r²), with df = n − 2. Its exact classical justification uses independent pairs from a bivariate normal population.

A p-value is conditional on that null model and the analysis assumptions. It is not the probability the correlation is “real,” and a threshold label does not establish importance. Sample size affects evidence and precision even though r is standardized.

Inspect the data before trusting one number

Plot the pairs to check curvature, clusters, and influential observations. Use the study design to assess independence. Repeated observations from a person or a time series may need a different inferential approach.

Do not treat the tool’s descriptive strength label as a universal practical threshold. A useful association depends on the setting and goal. Correlation alone does not establish causation, remove confounding, or prove predictive value.

Related learning

Begin with scatter-plot interpretation, learn Pearson’s calculation, or continue to linear regression. Keep pair identity intact in any exported data.