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	74.8									74.8
Other comprehensive (loss) income, net of tax	12.3												12.3
Exercise of stock options	5.3							5.3
Share-based compensation	6.5							6.5
Ending balance at Mar. 31, 2021	860.2			0.2		(57.6)		304.4		641.0			(27.8)
Beginning balance at Dec. 31, 2020	799.5			0.2		(57.6)		297.4		585.7			(26.2)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	55.3									55.3
Other comprehensive (loss) income, net of tax	(1.6)												(1.6)
Exercise of stock options	3.6							3.6
Share-based compensation	3.4							3.4
Ending balance at Mar. 31, 2021	860.2			0.2		(57.6)		304.4		641.0			(27.8)
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]
Other comprehensive (loss) income, net of tax	(1.4)
Ending balance at Dec. 31, 2021	953.0			0.2		(69.3)		324.4		724.2			(26.5)
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	105.7									105.7
Other comprehensive (loss) income, net of tax	(18.3)												(18.3)
Exercise of stock options	5.9							5.9
Share-based compensation	8.3							8.3
Ending balance at Mar. 31, 2022	1,005.6			0.2		(69.3)		329.9		788.2			(43.4)
Beginning balance at Dec. 31, 2021	953.0			0.2		(69.3)		324.4		724.2			(26.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	64.0									64.0
Other comprehensive (loss) income, net of tax	(16.9)												(16.9)
Exercise of stock options	1.3							1.3
Share-based compensation	4.2							4.2
Ending balance at Mar. 31, 2022	$ 1,005.6			$ 0.2		$ (69.3)		$ 329.9		$ 788.2			$ (43.4)