Earnings Per Share - Schedule of Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended						9 Months Ended
	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Jul. 31, 2019	Jul. 31, 2018
Earnings Per Share [Abstract]
Net income	$ 120.1	$ 122.4	$ 103.2	$ 100.8	$ 60.9	$ (122.5)	$ 345.7	$ 39.2
Basic:
Weighted average common shares (in shares)	49.5			49.1			49.4	49.0
Basic earnings per share (in dollars per share)	$ 2.43			$ 2.05			$ 7.00	$ 0.80
Diluted:
Effect of potential dilutive shares (in shares)	0.6			0.6			0.6	0.6
Diluted weighted average common shares (in shares)	50.1			49.7			50.0	49.6
Diluted earnings per share attributable to Cooper stockholders (in dollars per share)	$ 2.40			$ 2.03			$ 6.91	$ 0.79