Business Segment Information - Sales and Operating Results (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jun. 30, 2024	Jun. 30, 2023	Jun. 30, 2024	Jun. 30, 2023
Sales and operating results of reportable segments
Sales	$ 2,050.6	$ 2,238.7	$ 6,228.7	$ 6,495.1
Purchase accounting depreciation and amortization	(35.6)	(27.2)	(108.3)	(79.8)
Corporate and other	(28.6)	(32.3)	(96.8)	(88.8)
Non-operating pension and postretirement benefit credit (cost)	4.9	5.5	14.7	(87.5)
Change in fair value of investments	(5.0)	85.7	0.9	289.3
Restructuring charges	(69.8)	0.0	(69.8)	0.0
Interest expense, net	(37.4)	(32.9)	(101.9)	(100.2)
Income before income taxes	255.0	471.8	825.0	1,291.1
Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	426.5	473.0	1,186.2	1,358.1
Intelligent Devices
Sales and operating results of reportable segments
Sales	957.3	968.1	2,858.1	2,927.5
Intelligent Devices | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	193.5	163.1	504.7	579.4
Software & Control
Sales and operating results of reportable segments
Sales	512.1	750.6	1,685.7	2,065.0
Software & Control | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	120.6	261.5	417.9	678.1
Lifecycle Services
Sales and operating results of reportable segments
Sales	581.2	520.0	1,684.9	1,502.6
Lifecycle Services | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	$ 112.4	$ 48.4	$ 263.6	$ 100.6