Goodwill and Indefinite-Lived Intangible Assets (Schedule of Goodwill Activity) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Goodwill [Line Items]
Goodwill	$ 2,273.7	$ 2,211.1	$ 2,232.4
Accumulated impairment losses	(472.8)	(472.8)	(472.8)
Goodwill [Roll Forward]
Goodwill, net	1,738.3	1,759.6
Goodwill related to acquisitions	(158.6)	(0.8)
Goodwill, Written off Related to Sale of Business Unit	(81.7)
Currency translation effect	(14.3)	(8.9)
Goodwill, net	1,800.9	1,738.3
Patient Support Systems [Member]
Goodwill [Line Items]
Goodwill	640.5	544.4	545.0
Accumulated impairment losses	(472.8)	(472.8)	472.8
Goodwill [Roll Forward]
Goodwill, net	71.6	72.2
Goodwill related to acquisitions	(98.4)	0.0
Currency translation effect	(2.3)	(0.6)
Goodwill, net	167.7	71.6
Front Line Care [Member]
Goodwill [Line Items]
Goodwill	1,424.7	1,370.6	1,375.6
Accumulated impairment losses	0.0	0.0
Goodwill [Roll Forward]
Goodwill, net	1,370.6	1,375.6
Goodwill related to acquisitions	(60.2)	(0.8)
Currency translation effect	(6.1)	(5.8)
Goodwill, net	1,424.7	1,370.6
Surgical Solutions [Member]
Goodwill [Line Items]
Goodwill	208.5	296.1	$ 311.8
Accumulated impairment losses	0.0	0.0
Goodwill [Roll Forward]
Goodwill, net	296.1	311.8
Goodwill related to acquisitions	0.0	0.0
Goodwill, Written off Related to Sale of Business Unit	(81.7)
Currency translation effect	(5.9)	(2.5)
Goodwill, net	$ 208.5	$ 296.1