Earnings Per Share - Schedule of Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended
	Jan. 31, 2020	Jan. 31, 2019
Earnings Per Share [Abstract]
Net income	$ 90.5	$ 103.2
Basic:
Weighted average common shares (in shares)	49.1	49.3
Basic earnings per share (in dollars per share)	$ 1.84	$ 2.09
Diluted:
Effect of potential dilutive shares (in shares)	0.6	0.6
Diluted weighted average common shares (in shares)	49.7	49.9
Diluted earnings per share attributable to Cooper stockholders (in dollars per share)	$ 1.82	$ 2.07