Stock-Based Compensation - Schedule of Stock-Based Compensation Expense (Income) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Equity-based compensation plans
Stock-based compensation expense	$ 30.2	$ 30.0	$ 26.9
Income tax benefit recognized for stock-based compensation	(3.6)	(4.9)	(5.8)
Stock-based compensation cost, net of tax	26.6	25.1	21.1
Stock options
Equity-based compensation plans
Stock-based compensation expense	6.8	6.9	6.6
Nonvested Stock Awards [Member]
Equity-based compensation plans
Stock-based compensation expense	15.8	15.0	13.7
Income tax benefit recognized for stock-based compensation	(3.1)	(2.1)	(3.0)
Performance Shares [Member]
Equity-based compensation plans
Stock-based compensation expense	6.7	7.1	6.4
Stock Appreciation Rights (SARs)
Equity-based compensation plans
Stock-based compensation expense	0.2	0.4	(0.2)
Restricted Stock Units (RSUs)
Equity-based compensation plans
Stock-based compensation expense	$ 0.7	$ 0.6	$ 0.4