Consolidated Statements of Stockholders’ Equity - USD ($) $ in Millions	Total	Cumulative Effect, Period of Adoption, Adjusted Balance [Member]	Common Stock [Member]	Common Stock [Member] Cumulative Effect, Period of Adoption, Adjusted Balance [Member]	Treasury Stock [Member]	Treasury Stock [Member] Cumulative Effect, Period of Adoption, Adjusted Balance [Member]	Additional Paid-in Capital [Member]	Additional Paid-in Capital [Member] Cumulative Effect, Period of Adoption, Adjusted Balance [Member]	Retained Earnings [Member]	Retained Earnings [Member] Cumulative Effect, Period of Adoption, Adjustment [Member]	Retained Earnings [Member] Cumulative Effect, Period of Adoption, Adjusted Balance [Member]	Accumulated Other Comprehensive Loss, Net [Member]	Accumulated Other Comprehensive Loss, Net [Member] Cumulative Effect, Period of Adoption, Adjustment [Member]	Accumulated Other Comprehensive Loss, Net [Member] Cumulative Effect, Period of Adoption, Adjusted Balance [Member]
Beginning balance at Sep. 30, 2017	$ 449.9		$ 0.2		$ (46.3)		$ 259.0		$ 261.5			$ (24.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	55.5								55.5
Other comprehensive loss	(8.6)											(8.6)
Exercise of stock options	1.9						1.9
Share-based compensation	6.6						6.6
Ending balance at Sep. 30, 2018	505.3		0.2		(46.3)		267.5		317.0			(33.1)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	85.1								85.1
Other comprehensive loss	(1.7)											(1.7)
Exercise of stock options	1.2						1.2
Share-based compensation	8.1						8.1
Repurchase of stock	(3.8)				(3.8)
Ending balance at Sep. 30, 2019	$ 594.2	$ 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]
Accounting Standards Update [Extensible List]	us-gaap:AccountingStandardsUpdate201802Member
Net income	$ 169.6								169.6
Other comprehensive 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		$ 0.2		$ (57.6)		$ 292.6		$ 572.4			$ (40.1)