Two judges rank six paintings in a school art show, with 1 for the best…

$r = \dfrac{S_{xy}}{\sqrt{S_{xx}\,S_{yy}}}$ and $-1 \le r \le 1$. From totals, the numerator is $n\sum xy - \sum x \sum y$. The denominator has the factors $n\sum x^2 - \left(\sum x\right)^2$ and $n\sum y^2 - \left(\sum y\right)^2$ under one root. $r$ is unchanged by a change of units, and for ranks $r_s = 1 - \dfrac{6\sum d^2}{n(n^2 - 1)}$.