How to Calculate Correlation Coefficients With an Equation

Calculating correlation coefficients with an equation is best done with the aid of a calculator.
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Pearson's r is a correlation coefficient used to measure the strength of association between two variables that fall into the interval ratio category. Interval ratio variables are those which have a numerical value and can be placed in rank order. This coefficient is used in statistics. There are other correlation coefficient equations, such as correlation determination, but the Pearson's r formula is most commonly used.

    View the following given information as an example:

    Covariance = 22.40

    Standard deviation x = 9.636

    Standard deviation y = 3.606

    Plug the given information into the following equation:

    Pearson's Correlation Coefficient r = covariance/(standard deviation x)(standard deviation y) or use r = Sxy/(S2x)(S2y).

    The result with the example is:

    r = 22.40/(9.636)(3.606)

    Calculate r = 22.40/(9.636)(3.606)

    r = 22.40/34.747

    r = .6446

    r = .65 (round to two digits)


    • The answer can be positive or negative. The positive or negative shows the direction of the relationship. The closer the answer is to -1 or +1 the stronger the relationship is between the variables.


    • If you are given the variances instead, you will need to use the following formula: r2 = covariance squared/(variance x)(variance y). Square root the answer. You will need to add a negative sign if the original covariance in the equation was negative.

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