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Accumulated Other Comprehensive Income (Loss) (Details) - USD ($)
$ in Millions
 12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Accumulated Other Comprehensive Income (Loss) [Line Items]      
Beginning balance $ 711.5 $ 669.3 $ 694.9
Total other comprehensive income (loss) 17.9 (4.1) (39.6)
Ending balance 810.1 711.5 669.3
Accumulated other comprehensive income (loss)      
Accumulated Other Comprehensive Income (Loss) [Line Items]      
Beginning balance (48.7) (44.6) (5.0)
Total other comprehensive income (loss) 17.9 (4.1) (39.6)
Ending balance (30.8) (48.7) $ (44.6)
Foreign currency translation, net of income tax      
Accumulated Other Comprehensive Income (Loss) [Line Items]      
Beginning balance (20.2)    
Total other comprehensive income (loss) 9.1    
Ending balance (11.1) (20.2)  
Pension liability, net of income tax      
Accumulated Other Comprehensive Income (Loss) [Line Items]      
Beginning balance (28.5)    
Total other comprehensive income (loss) 8.8    
Ending balance $ (19.7) $ (28.5)