Other (Income) Expense, Net (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021
Other Income and Expenses [Abstract]
Unrealized gain (loss) on company-owned life insurance contracts and investments held in rabbi trusts	$ 2.2	$ (1.2)	$ 0.0	$ (5.6)
Foreign exchange loss	0.7	0.4	1.3	3.9
Pension earnings, interest and deferrals (income) expense	(4.5)	0.2	(13.7)	2.2
Pension settlement charge	0.0	8.9	0.0	8.9
Other	(0.2)	0.0	(0.1)	0.0
Total other (income) expense, net	$ (1.8)	$ 8.3	$ (12.5)	$ 9.4