Goodwill and Intangible Assets, net - Changes in Goodwill (Details) $ in Millions	9 Months Ended
	Mar. 31, 2024 USD ($)
Goodwill [Roll Forward]
Balance at June 30, 2023	$ 2,339.4
Additions and other adjustments	24.5
Currency translation adjustments	(8.5)
Balance at March 31, 2024	2,355.4
Employer Services
Goodwill [Roll Forward]
Balance at June 30, 2023	2,334.6
Additions and other adjustments	24.5
Currency translation adjustments	(8.5)
Balance at March 31, 2024	2,350.6
PEO Services
Goodwill [Roll Forward]
Balance at June 30, 2023	4.8
Additions and other adjustments	0.0
Currency translation adjustments	0.0
Balance at March 31, 2024	$ 4.8