Business Segment Information - Sales and Operating Results (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended		12 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021	Sep. 30, 2021
Sales and operating results of reportable segments
Sales	$ 1,808.1	$ 1,776.1	$ 3,665.4	$ 3,341.4
Purchase accounting depreciation and amortization	(26.1)	(13.1)	(52.2)	(24.8)
Corporate and other	(24.6)	(30.4)	(54.0)	(58.4)
Non-operating pension and postretirement benefit cost	(21.3)	(7.0)	(16.9)	(14.0)
Change in fair value of investments	(140.7)	190.9	(133.1)	581.3
Legal settlement	0.0	0.0	0.0	70.0
Interest expense, net	(29.6)	(22.8)	(58.7)	(45.1)
Income before income taxes	41.1	507.7	323.6	1,208.4
Gain (loss) related to litigation settlement	70.0				$ 70.0
Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	283.4	390.1	638.5	699.4
Intelligent Devices
Sales and operating results of reportable segments
Sales	808.6	850.2	1,708.9	1,571.9
Intelligent Devices | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	118.2	202.0	331.2	342.2
Software & Control
Sales and operating results of reportable segments
Sales	534.9	502.3	1,048.8	943.3
Software & Control | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	131.5	149.8	249.1	282.9
Lifecycle Services
Sales and operating results of reportable segments
Sales	464.6	423.6	907.7	826.2
Lifecycle Services | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	$ 33.7	$ 38.3	$ 58.2	$ 74.3