Condensed Consolidated Statements of Stockholders' Equity - USD ($) $ in Millions	Total	Cumulative Effect, Period of Adoption, Adjustment	Cumulative Effect, Period of Adoption, Adjusted Balance	Common Stock	Common Stock Cumulative Effect, Period of Adoption, Adjusted Balance	Treasury Stock	Treasury Stock Cumulative Effect, Period of Adoption, Adjusted Balance	Additional Paid-in Capital	Additional Paid-in Capital Cumulative Effect, Period of Adoption, Adjusted Balance	Retained Earnings	Retained Earnings Cumulative Effect, Period of Adoption, Adjustment	Retained Earnings Cumulative Effect, Period of Adoption, Adjusted Balance	Accumulated Other Comprehensive Loss, net	Accumulated Other Comprehensive Loss, net Cumulative Effect, Period of Adoption, Adjusted Balance
Beginning 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]
Net income	109.0									109.0
Other comprehensive (loss) income, net of tax	16.3												16.3
Exercise of stock options	7.6							7.6
Share-based compensation	10.3							10.3
Repurchase of common stock	(3.1)					(3.1)
Ending balance at Jun. 30, 2021	901.4			0.2		(60.7)		310.5		675.2			(23.8)
Beginning balance at Mar. 31, 2021	860.2			0.2		(57.6)		304.4		641.0			(27.8)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	34.2									34.2
Other comprehensive (loss) income, net of tax	4.0												4.0
Exercise of stock options	2.3							2.3
Share-based compensation	3.8							3.8
Repurchase of common stock	(3.1)					(3.1)
Ending balance at Jun. 30, 2021	901.4			0.2		(60.7)		310.5		675.2			(23.8)
Beginning 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	154.8									154.8
Other comprehensive (loss) income, net of tax	(30.5)												(30.5)
Exercise of stock options	6.2							6.2
Share-based compensation	12.8							12.8
Ending balance at Jun. 30, 2022	1,047.3			0.2		(69.3)		334.7		837.3			(55.6)
Beginning balance at Mar. 31, 2022	1,005.6			0.2		(69.3)		329.9		788.2			(43.4)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	49.1									49.1
Other comprehensive (loss) income, net of tax	(12.2)												(12.2)
Exercise of stock options	0.3							0.3
Share-based compensation	4.5							4.5
Ending balance at Jun. 30, 2022	$ 1,047.3			$ 0.2		$ (69.3)		$ 334.7		$ 837.3			$ (55.6)