Fair Value Measurements - Schedule of Assets and Liabilities Measured at Fair Value on a Recurring and Nonrecurring Basis (Details) - USD ($) $ in Millions	3 Months Ended		12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Jun. 30, 2020
Nonrecurring fair value measurements
Total losses	$ 0.0	$ (9.5)
Measured at fair value on recurring basis
Recurring fair value measurements
Cash and cash equivalents - cash equivalents	102.9		$ 115.2
Accrued expenses
Contingent consideration	2.2		1.3
Deferred compensation plans	2.4		3.4
Other noncurrent liabilities
Contingent consideration	2.7		3.6
Deferred compensation plans	14.0		13.5
Total recurring liability fair value measurements	21.3		21.8
Measured at fair value on recurring basis | Level 1
Recurring fair value measurements
Cash and cash equivalents - cash equivalents	102.9		115.2
Accrued expenses
Contingent consideration	0.0		0.0
Deferred compensation plans	0.0		0.0
Other noncurrent liabilities
Contingent consideration	0.0		0.0
Deferred compensation plans	0.0		0.0
Total recurring liability fair value measurements	0.0		0.0
Measured at fair value on recurring basis | Level 2
Recurring fair value measurements
Cash and cash equivalents - cash equivalents	0.0		0.0
Accrued expenses
Contingent consideration	0.0		0.0
Deferred compensation plans	2.4		3.4
Other noncurrent liabilities
Contingent consideration	0.0		0.0
Deferred compensation plans	14.0		13.5
Total recurring liability fair value measurements	16.4		16.9
Measured at fair value on recurring basis | Level 3
Recurring fair value measurements
Cash and cash equivalents - cash equivalents	0.0		0.0
Accrued expenses
Contingent consideration	2.2		1.3
Deferred compensation plans	0.0		0.0
Other noncurrent liabilities
Contingent consideration	2.7		3.6
Deferred compensation plans	0.0		0.0
Total recurring liability fair value measurements	$ 4.9		4.9
Measured at fair value on nonrecurring basis
Nonrecurring fair value measurements
Intangible assets, net			0.0
Measured at fair value on nonrecurring basis | Level 1
Nonrecurring fair value measurements
Intangible assets, net			0.0
Measured at fair value on nonrecurring basis | Level 2
Nonrecurring fair value measurements
Intangible assets, net			0.0
Measured at fair value on nonrecurring basis | Level 3
Nonrecurring fair value measurements
Intangible assets, net			0.0
Intangible Assets, Net | Measured at fair value on nonrecurring basis
Nonrecurring fair value measurements
Total losses			$ (5.2)