Goodwill and Indefinite-Lived Intangible Assets (Schedule of Goodwill Activity) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Goodwill [Line Items]
Goodwill	$ 2,308.3	$ 2,273.7	$ 2,211.1
Accumulated impairment losses	(472.8)	(472.8)	(472.8)
Goodwill [Roll Forward]
Goodwill, net	1,800.9	1,738.3
Goodwill related to acquisitions	(25.0)	(158.6)
Currency translation effect	9.6	(14.3)
Goodwill, net	1,835.5	1,800.9
Patient Support Systems [Member]
Goodwill [Line Items]
Goodwill	653.5	640.5	544.4
Accumulated impairment losses	(472.8)	472.8	472.8
Goodwill [Roll Forward]
Goodwill, net	167.7	71.6
Goodwill related to acquisitions	(10.6)	98.4
Currency translation effect	2.4	(2.3)
Goodwill, net	180.7	167.7
Front Line Care [Member]
Goodwill [Line Items]
Goodwill	1,432.6	1,424.7	1,370.6
Accumulated impairment losses	0.0	0.0
Goodwill [Roll Forward]
Goodwill, net	1,424.7	1,370.6
Goodwill related to acquisitions	(4.4)	(60.2)
Currency translation effect	3.5	(6.1)
Goodwill, net	1,432.6	1,424.7
Surgical Solutions [Member]
Goodwill [Line Items]
Goodwill	222.2	208.5	$ 296.1
Accumulated impairment losses	0.0	0.0
Goodwill [Roll Forward]
Goodwill, net	208.5	296.1
Goodwill related to acquisitions	(10.0)	81.7
Goodwill, Written off Related to Sale of Business Unit	10.0
Currency translation effect	3.7	(5.9)
Goodwill, net	$ 222.2	$ 208.5