Selected Quarterly Financial Data (Unaudited) - Schedule of Quarterly Financial Data (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2017
Quarterly Financial Information Disclosure [Abstract]
Net sales	$ 691.6	$ 679.4	$ 654.3	$ 628.1	$ 651.5	$ 660.0	$ 631.3	$ 590.0	$ 2,653.4	$ 2,532.8	$ 2,139.0
Gross profit	455.0	450.7	432.6	418.5	430.0	426.8	404.5	370.9	1,756.8	1,632.3	1,365.8
Income before income taxes	128.5	127.0	128.1	93.8	112.7	90.4	54.0	74.8
Net (loss) income attributable to Cooper stockholders	$ 121.0	$ 120.1	$ 122.4	$ 103.2	$ 100.6	$ 100.8	$ 60.9	$ (122.5)	$ 466.7	$ 139.9	$ 372.9
Basic earnings per share attributable to Cooper stockholders (in dollars per share)	$ 2.44	$ 2.43	$ 2.48	$ 2.09	$ 2.05	$ 2.05	$ 1.24	$ (2.50)	$ 9.44	$ 2.85	$ 7.63
Diluted earnings per share attributable to Cooper stockholders (in dollars per share)	$ 2.42	$ 2.40	$ 2.45	$ 2.07	$ 2.02	$ 2.03	$ 1.23	$ (2.50)	$ 9.33	$ 2.81	$ 7.52