Earnings Per Share - Basic and Diluted (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	12 Months Ended
	Oct. 31, 2021	Oct. 31, 2020	Oct. 31, 2019
Earnings Per Share [Abstract]
Net income, basic	$ 2,944.7	$ 238.4	$ 466.7
Net income, diluted	$ 2,944.7	$ 238.4	$ 466.7
Basic:
Weighted average common shares (in shares)	49.2	49.1	49.4
Basic earnings per share attributable to Cooper stockholders (in dollars per share)	$ 59.80	$ 4.85	$ 9.44
Diluted:
Effect of dilutive stock options (in shares)	0.6	0.5	0.6
Diluted weighted average common shares (in shares)	49.8	49.6	50.0
Diluted earnings per share attributable to Cooper stockholders (in dollars per share)	$ 59.16	$ 4.81	$ 9.33