Income Taxes - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Income Tax Disclosure [Abstract]
Income tax liabilities	$ 97.0
Income tax paid	78.0	$ 58.0	$ 31.0
Tax benefit attributable to non-U.S. government sponsored tax incentive programs	$ 45.0	$ 36.0	$ 62.0
Tax benefit per diluted share attributable to non-U.S. government sponsored tax incentive programs (in usd per share)	$ 0.40	$ 0.31	$ 0.54
Undistributed earnings of foreign subsidiaries	$ 156.0
Gross unrecognized tax benefits	29.0	$ 25.0	$ 10.0	$ 4.0
Accrued interest and penalties for unrecognized tax benefits	2.0	2.0	1.0
Benefits (expense) recognized for interest and penalties related to unrecognized tax benefits	0.0	$ (1.0)	$ 0.0
Reasonably possible amount of reduction of gross unrecognized tax benefit in the next twelve months	24.0
Reasonably possible amount of net reduction to income tax provision in the next twelve months if unrecognized tax benefits were recognized, including the recognition of interest and penalties and offsetting tax assets	$ 25.0