If S is the stock return and M is the market return, then Beta = cor(S,M)*vol(S)/vol(M) Where cor(A,B) is correlation between A and B, and vol(X) is volatilit

If S is the stock return and M is the market return, then Beta = cor(S,M)*vol(S)/vol(M) Where cor(A,B) is correlation between A and B, and vol(X) is volatility of X (i.e. standard deviation).