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Formula verified · Deterministic calculation

Correlation Calculator

Enter two equal-length numeric datasets to measure their linear association with Pearson's correlation coefficient.

Pearson correlation (r)1
Paired observations3
Mean of X2
Mean of Y4
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Result methodology

Pearson product-moment correlation calculated from paired deviations around each dataset mean.

Solution steps
  1. n = 3; mean(x) = 2; mean(y) = 4
  2. r = Σ((x-x̄)(y-ȳ))/√(Σ(x-x̄)²Σ(y-ȳ)²) = 0.9999999999999998

How this calculator works

Pearson r divides the paired cross-deviation sum by the geometric mean of the two deviation sums of squares.

Formula

r=Σ((x−x̄)(y−ȳ))/√(Σ(x−x̄)²Σ(y−ȳ)²)

Calculates the Pearson product-moment correlation coefficient for paired numeric observations.

Worked example

Perfect positive relationship is a verified test case used by the calculation engine.

Assumptions and limitations

  • Datasets contain paired observations and have equal length.
  • At least two pairs are required.
  • Correlation is undefined when either dataset is constant.
  • Correlation measures linear association and does not establish causation.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic statistics engine

Frequently asked questions

What range can Pearson r take?

The coefficient ranges from −1 to 1.

Does correlation prove causation?

No. Correlation quantifies linear association; it does not by itself establish a causal relationship.

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Mean Median Mode Range CalculatorCalculate mean, median, mode, minimum, maximum and range from a dataset.Standard Deviation CalculatorCalculate population or sample standard deviation and variance.Linear Regression CalculatorFit a least-squares line to paired numeric observations.