Earnings Per Share (Schedule of Earnings Per Share) (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended				6 Months Ended
	Apr. 30, 2019	Jan. 31, 2019	Apr. 30, 2018	Jan. 31, 2018	Apr. 30, 2019	Apr. 30, 2018
Earnings Per Share [Abstract]
Net income (loss)	$ 122.4	$ 103.2	$ 60.9	$ (122.5)	$ 225.5	$ (61.6)
Basic:
Weighted average common shares	49.4		49.1		49.3	49.0
Basic earnings (loss) per share	$ 2.48		$ 1.24		$ 4.57	$ (1.26)
Diluted:
Effect of potential dilutive shares	0.6		0.5		0.6	0.0
Diluted weighted average common shares	50.0		49.6		49.9	49.0
Diluted earnings (loss) per share attributable to Cooper stockholders	$ 2.45		$ 1.23		$ 4.52	$ (1.26)