Third Party Arrangements and Related Party Disclosures - Net Transfers to Parent (Details) $ in Millions	3 Months Ended
	Dec. 31, 2021 USD ($)
Third Party and Related Party Transactions [Abstract]
Cash pooling and general financing activities	$ 170.3
Corporate and segment allocations, excluding non-cash stock-based compensation	(25.1)
Taxes deemed settled with BD	(10.7)
Net transfers to BD as reflected in the Condensed Consolidated Statements of Cash Flows	134.5
Stock-based compensation expense	(4.6)
Pension expense	(2.2)
Other transfers to (from) BD, net	6.1
Net transfers to BD	$ 133.8