Correlation and Beta market, standard, mkt

wonderfuldream

When calculating the correlation coefficient

P1,2 = (COV1,2) / (standard deviation 1) X (standard deviation 2)

(given that 1 is stock 1 and 2 is stock 2)

Now, when considering beta; we standardize the systematic risk in units of "market risk" by:

Beta1 = (COV1,mkt) / (variance mkt)

What I want to know is why in the correlation formula standard deviation is in the denominator and when calculating beta, variance is used in the denominator?