Accumulated Other Comprehensive Loss, Net (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	$ 1,379.1	$ 1,070.1
Other comprehensive income, net of tax	27.6	22.9
Ending balance	1,482.8	1,176.6
Foreign Currency Translation Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(31.2)
Other comprehensive income, net of tax	6.9
Ending balance	(24.3)
Pension Benefits Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(2.2)
Other comprehensive income, net of tax	0.0
Ending balance	(2.2)
Cash Flow Hedge
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(18.4)
Other comprehensive income, net of tax	20.7
Ending balance	2.3
Accumulated Other Comprehensive Loss, net
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(51.8)	(90.6)
Other comprehensive income, net of tax	27.6	22.9
Ending balance	$ (24.2)	$ (67.7)