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, 2020	Apr. 30, 2020	Jan. 31, 2020	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Jul. 31, 2020	Jul. 31, 2019
Earnings Per Share [Abstract]
Net income	$ 55.2	$ 11.5	$ 90.5	$ 120.1	$ 122.4	$ 103.2	$ 157.2	$ 345.7
Basic:
Weighted average common shares (in shares)	49.1			49.5			49.1	49.4
Basic earnings per share (in dollars per share)	$ 1.13			$ 2.43			$ 3.20	$ 7.00
Diluted:
Weighted average common shares (in shares)	49.1			49.5			49.1	49.4
Effect of potential dilutive shares (in shares)	0.4			0.6			0.5	0.6
Diluted weighted average common shares (in shares)	49.5			50.1			49.6	50.0
Diluted earnings per share attributable to Cooper stockholders (in dollars per share)	$ 1.12			$ 2.40			$ 3.17	$ 6.91