Why do the units of measurement affect covariance but not correlation?

The magnitude of covariance is expressed in the product of the variables' units of measurement, making it dependent on the scale of the data. For example, if one measures age in years and height in centimeters, the resulting covariance is expressed in "centimeter-years," which is often uninformative and lacks a standardized bound.1

In contrast, correlation is a normalized version of covariance. The correlation coefficient is calculated by dividing the covariance by the product of the variables' standard deviations. Because standard deviations are expressed in the same units as their respective variables, this division effectively cancels out the units of measurement. As a result, the correlation coefficient is a dimensionless value that always falls between −1 and 1, allowing it to indicate the strength and direction of a linear relationship regardless of the original units used.213