Consolidated Statements of Stockholders’ Equity - USD ($) $ in Millions	Total	Cumulative transition adjustment	Adjusted balance	Common Stock	Common Stock Adjusted balance	Treasury Stock	Treasury Stock Adjusted balance	Additional Paid-in Capital	Additional Paid-in Capital Adjusted balance	Retained Earnings	Retained Earnings Cumulative transition adjustment	Retained Earnings Adjusted balance	Accumulated Other Comprehensive Loss, net	Accumulated Other Comprehensive Loss, net Cumulative transition adjustment	Accumulated Other Comprehensive Loss, net Adjusted balance
Beginning balance at Sep. 30, 2019	$ 594.2	$ 0.0	$ 594.2	$ 0.2	$ 0.2	$ (50.1)	$ (50.1)	$ 276.8	$ 276.8	$ 402.1	$ 0.7	$ 402.8	$ (34.8)	$ (0.7)	$ (35.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	169.6									169.6
Other comprehensive income (loss)	(4.6)												(4.6)
Exercise of stock options	5.5							5.5
Share-based compensation	10.3							10.3
Repurchase of stock	(7.5)					(7.5)
Ending balance at Sep. 30, 2020	$ 767.5	$ (6.2)	$ 761.3	0.2	$ 0.2	(57.6)	$ (57.6)	292.6	$ 292.6	572.4	$ (6.2)	$ 566.2	(40.1)		$ (40.1)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Accounting Standards Update [Extensible Enumeration]	Accounting Standards Update 2016-13 [Member]
Net income	$ 116.3									116.3
Other comprehensive income (loss)	15.0												15.0
Exercise of stock options	9.2							9.2
Share-based compensation	13.9							13.9
Repurchase of stock	(11.7)					(11.7)
Ending balance at Sep. 30, 2021	904.0			0.2		(69.3)		315.7		682.5			(25.1)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	207.1									207.1
Other comprehensive income (loss)	(65.5)												(65.5)
Exercise of stock options	6.7							6.7
Share-based compensation	17.8							17.8
Ending balance at Sep. 30, 2022	$ 1,070.1			$ 0.2		$ (69.3)		$ 340.2		$ 889.6			$ (90.6)