Earnings Per Share - Schedule of Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ 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
Earnings Per Share [Abstract]
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:
Weighted average common shares (in shares)									49.4	49.1	48.9
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:
Effect of dilutive stock options (in shares)									0.6	0.6	0.7
Diluted weighted average common shares (in shares)									50.0	49.7	49.6
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