There are several types of correlation coefficient formulas.
One of the most commonly used formulas in stats is Pearson’s correlation coefficient formula. If you’re taking a basic stats class, this is the one you’ll probably use:
Pearson correlation coefficient
Two other formulas are commonly used: the sample correlation coefficient and the population correlation coefficient.
Sample correlation coefficient
Sx and sy are the sample standard deviations, and sxy is the sample covariance.
Population correlation coefficient
The population correlation coefficient uses σx and σy as the population standard deviations, and σxy as the population covariance.