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Accumulated Other Comprehensive Loss, Net (Details) - USD ($)
$ in Millions
 12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance $ 1,379.1 $ 1,070.1 $ 904.0
Other comprehensive income/(loss) net of tax 26.6 38.8 (65.5)
Ending balance 1,709.1 1,379.1 1,070.1
Foreign Currency Translation Adjustment      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (31.2) (34.4) (22.7)
Other comprehensive income/(loss) net of tax (0.1) 3.2 (11.7)
Ending balance (31.3) (31.2) (34.4)
Pension Benefits Adjustment      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (2.2) (2.7) (2.4)
Other comprehensive income/(loss) net of tax 1.0 0.5 (0.3)
Ending balance (1.2) (2.2) (2.7)
Cash Flow Hedge      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (18.4) (53.5) 0.0
Other comprehensive income/(loss) net of tax 25.7 35.1 (53.5)
Ending balance 7.3 (18.4) (53.5)
Accumulated Other Comprehensive Loss, net      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (51.8) (90.6) (25.1)
Other comprehensive income/(loss) net of tax 26.6 38.8 (65.5)
Ending balance $ (25.2) $ (51.8) $ (90.6)