Goodwill and Indefinite-Lived Intangible Assets (Schedule of Goodwill Activity) (Details) - USD ($)	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Goodwill [Line Items]
Goodwill	$ 2,694.5	$ 2,308,300,000	$ 2,273,700,000
Accumulated impairment losses	(472.8)	(472,800,000)	(472,800,000)
Goodwill [Roll Forward]
Goodwill, net	1,835,500,000	1,800,900,000
Goodwill related to acquisitions	(383.3)	(25,000,000.0)
Currency translation effect	2.9	9,600,000
Goodwill, net	2,221.7	1,835,500,000
Patient Support Systems [Member]
Goodwill [Line Items]
Goodwill	652.1	653,500,000	640,500,000
Accumulated impairment losses	(472.8)	472,800,000	472,800,000
Goodwill [Roll Forward]
Goodwill, net	180,700,000	167,700,000
Goodwill related to acquisitions	0.6	10,600,000
Currency translation effect	(0.8)	2,400,000
Goodwill, net	179.3	180,700,000
Front Line Care [Member]
Goodwill [Line Items]
Goodwill	1,820.3	1,432,600,000	1,424,700,000
Accumulated impairment losses	0	0
Goodwill [Roll Forward]
Goodwill, net	1,432,600,000	1,424,700,000
Goodwill related to acquisitions	(383.8)	(4,400,000)
Currency translation effect	3.9	3,500,000
Goodwill, net	1,820.3	1,432,600,000
Surgical Solutions [Member]
Goodwill [Line Items]
Goodwill	222.1	222,200,000	$ 208,500,000
Accumulated impairment losses	0	0
Goodwill [Roll Forward]
Goodwill, net	222,200,000	208,500,000
Goodwill related to acquisitions	(0.1)	(10,000,000.0)
Goodwill, Written off Related to Sale of Business Unit	0.1
Currency translation effect	(0.2)	3,700,000
Goodwill, net	$ 222.1	$ 222,200,000