Third Party Arrangements and Related Party Disclosures - Net Transfers to Parent (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Third Party and Related Party Transactions [Abstract]
Cash pooling and general financing activities	$ 170.2	$ 255.9	$ 473.3
Corporate and segment allocations, excluding non-cash share-based compensation	(28.4)	(50.4)	(82.1)
Taxes deemed settled with BD	(19.8)	(16.2)	(46.3)
Other Separation related adjustments, net		(6.6)	0.0
Net transfers to BD as reflected in the Condensed Consolidated Statements of Cash Flows	122.0	182.7	344.9
Share-based compensation expense	(2.9)	(8.5)	(9.6)
Pension expense	(2.1)	(3.6)	(7.0)
Net Consideration paid to BD in connection with the Separation		1,266.0	0.0
Related party senior secured notes		197.0	0.0
Other transfers to (from) BD, net	(8.3)	84.1	(18.6)
Net transfers to BD	$ 108.7	$ 1,717.7	$ 309.7