Stock-Based Compensation Plans - Schedule of Stock-based Compensation Expense (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense, pre-tax	$ 13.8	$ 9.9	$ 9.2
Tax benefit	(3.5)	(2.5)	(2.3)
Total stock-based compensation expense, net of tax	10.3	7.4	6.9
Stock appreciation rights
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense, pre-tax	1.2	1.5	1.3
Nonvested Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense, pre-tax	$ 12.6	$ 8.4	$ 7.9