Consolidated Condensed Statements of Stockholders' Equity - USD ($) $ in Millions	Total	Cumulative Effect, Period of Adoption, Adjustment	Common Shares	Treasury Stock	Treasury Stock Par Net Value	Additional Paid-In Capital	Accumulated Other Comprehensive Income (Loss)	Retained Earnings	Retained Earnings Cumulative Effect, Period of Adoption, Adjustment	Noncontrolling Interests
Beginning balance (in shares) at Oct. 31, 2019			49,100,000	4,100,000
Beginning balance at Oct. 31, 2019	$ 3,628.6		$ 4.9	$ (571.2)	$ 0.4	$ 1,615.0	$ (447.1)	$ 3,026.4		$ 0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income attributable to Cooper stockholders	90.5							90.5
Other comprehensive income (loss), net of tax	16.7						16.7
Issuance of common stock for stock plans, net (in shares)			100,000
Issuance of common stock for stock plans, net	(13.1)					(13.2)
Dividends on common stock ($0.03 per share)	(1.5)							(1.5)
Share-based compensation expense	9.7					9.7
Ending balance (in shares) at Jan. 31, 2020			49,200,000	4,100,000
Ending balance at Jan. 31, 2020	3,730.9		$ 4.9	$ (571.2)	0.4	1,611.6	(430.4)	3,115.4		0.2
Beginning balance (in shares) at Oct. 31, 2019			49,100,000	4,100,000
Beginning balance at Oct. 31, 2019	3,628.6		$ 4.9	$ (571.2)	0.4	1,615.0	(447.1)	3,026.4		0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income attributable to Cooper stockholders	$ 102.0
Treasury stock repurchase (in shares)	160,800
Treasury stock repurchase	$ (47.8)
Ending balance (in shares) at Apr. 30, 2020			49,100,000	4,300,000
Ending balance at Apr. 30, 2020	3,627.5		$ 4.9	$ (618.6)	0.4	1,626.5	(512.8)	3,126.9		0.2
Beginning balance (in shares) at Oct. 31, 2019			49,100,000	4,100,000
Beginning balance at Oct. 31, 2019	$ 3,628.6		$ 4.9	$ (571.2)	0.4	1,615.0	(447.1)	3,026.4		0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Accounting Standards Update [Extensible List]	us-gaap:AccountingStandardsUpdate201613Member
Ending balance (in shares) at Oct. 31, 2020	49,100,000		49,100,000	4,300,000
Ending balance at Oct. 31, 2020	$ 3,824.8	$ (1.4)	$ 4.9	$ (617.3)	0.4	1,646.8	(472.0)	3,261.8	$ (1.4)	0.2
Beginning balance (in shares) at Jan. 31, 2020			49,200,000	4,100,000
Beginning balance at Jan. 31, 2020	3,730.9		$ 4.9	$ (571.2)	0.4	1,611.6	(430.4)	3,115.4		0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income attributable to Cooper stockholders	11.5							11.5
Other comprehensive income (loss), net of tax	(82.4)						(82.4)
Issuance of common stock for stock plans, net (in shares)			100,000
Issuance of common stock for stock plans, net	5.0					5.0
Issuance of common stock for employee stock purchase plan	1.0			$ 0.4		0.6
Share-based compensation expense	9.3					9.3
Treasury stock repurchase (in shares)			200,000	200,000
Treasury stock repurchase	(47.8)			$ (47.8)
Ending balance (in shares) at Apr. 30, 2020			49,100,000	4,300,000
Ending balance at Apr. 30, 2020	$ 3,627.5		$ 4.9	$ (618.6)	0.4	1,626.5	(512.8)	3,126.9		0.2
Beginning balance (in shares) at Oct. 31, 2020	49,100,000		49,100,000	4,300,000
Beginning balance at Oct. 31, 2020	$ 3,824.8	(1.4)	$ 4.9	$ (617.3)	0.4	1,646.8	(472.0)	3,261.8	(1.4)	0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income attributable to Cooper stockholders	2,101.1							2,101.1
Other comprehensive income (loss), net of tax	90.7						90.7
Issuance of common stock for stock plans, net (in shares)			100,000
Issuance of common stock for stock plans, net	(11.0)					(11.0)
Issuance of common stock for employee stock purchase plan	1.4			$ 0.6		0.8
Dividends on common stock ($0.03 per share)	(1.5)							(1.5)
Share-based compensation expense	10.6					10.6
Treasury stock repurchase (in shares)			100,000	100,000
Treasury stock repurchase	(24.8)			$ (24.8)
Ending balance (in shares) at Jan. 31, 2021			49,100,000	4,400,000
Ending balance at Jan. 31, 2021	$ 5,989.9		$ 4.9	$ (641.5)	0.4	1,647.2	(381.3)	5,360.0		0.2
Beginning balance (in shares) at Oct. 31, 2020	49,100,000		49,100,000	4,300,000
Beginning balance at Oct. 31, 2020	$ 3,824.8	$ (1.4)	$ 4.9	$ (617.3)	0.4	1,646.8	(472.0)	3,261.8	$ (1.4)	0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income attributable to Cooper stockholders	$ 2,218.6
Treasury stock repurchase (in shares)	69,600
Treasury stock repurchase	$ (24.8)
Ending balance (in shares) at Apr. 30, 2021	49,200,000		49,200,000	4,400,000
Ending balance at Apr. 30, 2021	$ 6,162.8		$ 5.0	$ (640.9)	0.4	1,667.8	(347.2)	5,477.5		0.2
Beginning balance (in shares) at Jan. 31, 2021			49,100,000	4,400,000
Beginning balance at Jan. 31, 2021	5,989.9		$ 4.9	$ (641.5)	0.4	1,647.2	(381.3)	5,360.0		0.2
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income attributable to Cooper stockholders	117.5							117.5
Other comprehensive income (loss), net of tax	34.1						34.1
Issuance of common stock for stock plans, net (in shares)			100,000
Issuance of common stock for stock plans, net	9.8		$ 0.1			9.7
Issuance of common stock for employee stock purchase plan	1.5			$ 0.6		0.9
Share-based compensation expense	$ 10.0					10.0
Treasury stock repurchase (in shares)	0
Ending balance (in shares) at Apr. 30, 2021	49,200,000		49,200,000	4,400,000
Ending balance at Apr. 30, 2021	$ 6,162.8		$ 5.0	$ (640.9)	$ 0.4	$ 1,667.8	$ (347.2)	$ 5,477.5		$ 0.2