Supplemental Operations and Cash Flow Information (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Supplemental Cash Flow Elements [Abstract]
Advertising expense	$ 61.3	$ 40.9	$ 22.6
Research and development expense	14.3	12.0	11.4
Interest paid	59.6	66.6	45.0
Income taxes paid	$ 93.2	$ 60.9	$ 34.6