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Correlation Calculator

Measure how closely two variables move together. Enter paired X and Y values to get the Pearson correlation coefficient r, the coefficient of determination r², the sample covariance and a plain-English description of the strength.

Quick examples

Separate with commas or spaces.

Same number of values as X, in matching order.

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Correlation coefficient (r)0.7746
Coefficient of determination (r²)
0.6
Strength
Strong positive
Sample covariance
1.5
Number of pairs
5

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      Formula

      r = Σ(x − x̄)(y − ȳ) ÷ √( Σ(x − x̄)² × Σ(y − ȳ)² )
      Sample covariance = Σ(x − x̄)(y − ȳ) ÷ (n − 1)

      How to use it

      1. Type the X values, separated by commas.
      2. Type the Y values in the same order, one for each X.
      3. Read r: its sign gives the direction and its size the strength.

      Worked examples

      X = 1, 2, 3, 4, 5 and Y = 2, 4, 5, 4, 5

      Correlation coefficient (r)
      0.7746
      Coefficient of determination (r²)
      0.6
      Strength
      Strong positive
      Sample covariance
      1.5
      Number of pairs
      5

      Price against units sold

      Correlation coefficient (r)
      -0.9928
      Strength
      Very strong negative
      Sample covariance
      -30.75

      Reading r

      r runs from −1 to 1. Positive means Y tends to rise as X rises; negative means it falls. A value of ±1 is a perfect straight line and 0 means no linear relationship.

      The labels used here are a common rule of thumb: 0.8 and above very strong, 0.6 to 0.8 strong, 0.4 to 0.6 moderate, 0.2 to 0.4 weak, below 0.2 very weak. What counts as strong varies by field. r² is the share of the variation in Y that a straight-line relationship with X accounts for.

      Cautions

      Correlation does not show that one thing causes the other; both may depend on something else. Pearson’s r only detects straight-line relationships, so a strong curve can still score near zero. A single outlier can move r a long way, so it is worth plotting the data. In Excel and Google Sheets the function is CORREL.

      Questions people ask

      What is the correlation between X = 1, 2, 3, 4, 5 and Y = 2, 4, 5, 4, 5?

      r = 0.7746, a strong positive correlation, with r² = 0.6.

      What is a strong correlation?

      As a rule of thumb, an r of about 0.6 or more in either direction is strong and 0.8 or more is very strong, but standards differ between fields.

      Can r be greater than 1?

      No. It always lies between −1 and 1. A value outside that range means a calculation error.

      Related calculators

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