Earnings Per Share - Basic and Diluted (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended								12 Months Ended
	Oct. 31, 2020	Jul. 31, 2020	Apr. 30, 2020	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2020	Oct. 31, 2019	Oct. 31, 2018
Earnings Per Share [Abstract]
Net income attributable to Cooper stockholders	$ 81.2	$ 55.2	$ 11.5	$ 90.5	$ 121.0	$ 120.1	$ 122.4	$ 103.2	$ 238.4	$ 466.7	$ 139.9
Basic:
Weighted average common shares (in shares)									49.1	49.4	49.1
Basic earnings per share attributable to Cooper stockholders (in dollars per share)	$ 1.65	$ 1.13	$ 0.23	$ 1.84	$ 2.44	$ 2.43	$ 2.48	$ 2.09	$ 4.85	$ 9.44	$ 2.85
Diluted:
Effect of dilutive stock options (in shares)									0.5	0.6	0.6
Diluted weighted average common shares (in shares)									49.6	50.0	49.7
Diluted earnings per share attributable to Cooper stockholders (in dollars per share)	$ 1.64	$ 1.12	$ 0.23	$ 1.82	$ 2.42	$ 2.40	$ 2.45	$ 2.07	$ 4.81	$ 9.33	$ 2.81