Selected Quarterly Financial Data (Unaudited) (Details) - USD ($) $ / shares in Units, $ 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
Quarterly Financial Information Disclosure [Abstract]
Net sales	$ 681.6	$ 578.2	$ 524.9	$ 646.2	$ 691.6	$ 679.4	$ 654.3	$ 628.1	$ 2,430.9	$ 2,653.4	$ 2,532.8
Gross profit	424.0	360.8	323.5	426.5	455.0	450.7	432.6	418.5	1,534.8	1,756.8	1,632.3
Income before income taxes	93.7	66.4	9.0	97.4	128.5	127.0	128.1	93.8
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 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 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