Segment Reporting (Schedule of Segment Information) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Net Revenue - United States:
Revenues	$ 705.3	$ 767.5	$ 723.2	$ 685.0	$ 782.8	$ 726.8	$ 714.2	$ 683.5	$ 2,881.0	$ 2,907.3	$ 2,848.0
Divisional income:
Divisional income	66.2	135.3	87.3	78.9	94.1	69.9	81.3	70.8	367.7	316.1	289.4
Other operating costs:
Other operating costs	$ 66.2	$ 135.3	$ 87.3	$ 78.9	$ 94.1	$ 69.9	$ 81.3	$ 70.8	367.7	316.1	289.4
Special charge									41.5	28.4	77.6
Interest expense									(74.0)	(89.6)	(95.0)
Loss on extinguishment of debt									(15.6)	(3.0)	0.0
Investment income (expense) and other, net									(6.9)	(14.6)	2.8
Income before income taxes									271.2	208.6	197.2
Depreciation, Depletion and Amortization									178.8	194.8	196.5
Non-US [Member]
Net Revenue - United States:
Revenues									914.2	850.5	891.6
Corporate, Non-Segment [Member]
Other operating costs:
Depreciation, Depletion and Amortization									32.5	28.3	27.6
Patient Support Systems [Member]
Other operating costs:
Depreciation, Depletion and Amortization									43.5	36.2	37.4
Front Line Care [Member]
Other operating costs:
Depreciation, Depletion and Amortization									95.4	101.9	110.7
Surgical Solutions [Member]
Other operating costs:
Depreciation, Depletion and Amortization									7.4	28.4	20.8
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Non-allocated operating costs, administrative and other									264.4	283.0	224.1
Operating Segments [Member]
Net Revenue - United States:
Revenues									2,881.0	2,907.3	2,848.0
Operating Segments [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues									1,966.8	2,056.8	1,956.4
Operating Segments [Member] | Non-US [Member]
Net Revenue - United States:
Revenues									914.2	850.5	891.6
Operating Segments [Member] | Patient Support Systems [Member]
Net Revenue - United States:
Revenues									1,539.1	1,490.5	1,429.5
Divisional Income									332.3	299.9	285.0
Operating Segments [Member] | Patient Support Systems [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues									1,133.6	1,135.0	1,054.6
Operating Segments [Member] | Patient Support Systems [Member] | Non-US [Member]
Net Revenue - United States:
Revenues									405.5	355.5	374.9
Operating Segments [Member] | Front Line Care [Member]
Net Revenue - United States:
Revenues									1,025.0	978.1	960.2
Divisional Income									301.8	266.4	253.0
Operating Segments [Member] | Front Line Care [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues									707.4	700.6	680.3
Operating Segments [Member] | Front Line Care [Member] | Non-US [Member]
Net Revenue - United States:
Revenues									317.6	277.5	279.9
Operating Segments [Member] | Surgical Solutions [Member]
Net Revenue - United States:
Revenues									316.9	438.7	458.3
Divisional Income									39.5	61.2	53.1
Operating Segments [Member] | Surgical Solutions [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues									125.8	221.2	221.5
Operating Segments [Member] | Surgical Solutions [Member] | Non-US [Member]
Net Revenue - United States:
Revenues									$ 191.1	$ 217.5	$ 236.8