Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Jun. 30, 2024	Sep. 30, 2023
Other intangible assets
Amortized intangible assets, carrying amount	$ 1,583.4	$ 1,222.9
Amortized intangible assets, accumulated amortization	526.7	414.2
Amortized intangible assets, net	1,056.7	808.7
Total, carrying amount	1,627.1	1,266.6
Total, net	1,100.4	852.4
Goodwill and Other Intangible Assets (Textual) [Abstract]
Estimated amortization expense in 2023	153.3
Estimated amortization expense in 2024	149.8
Estimated amortization expense in 2025	148.5
Estimated amortization expense in 2026	140.4
Estimated amortization expense in 2027	127.8
Trademarks
Other intangible assets
Allen-Bradley trademark not subject to amortization	43.7	43.7
Software products
Other intangible assets
Amortized intangible assets, carrying amount	103.4	100.4
Amortized intangible assets, accumulated amortization	72.2	65.1
Amortized intangible assets, net	31.2	35.3
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	616.6	606.1
Amortized intangible assets, accumulated amortization	174.1	141.3
Amortized intangible assets, net	442.5	464.8
Technology
Other intangible assets
Amortized intangible assets, carrying amount	726.8	424.1
Amortized intangible assets, accumulated amortization	235.2	173.1
Amortized intangible assets, net	491.6	251.0
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	130.9	86.3
Amortized intangible assets, accumulated amortization	40.0	29.3
Amortized intangible assets, net	90.9	57.0
Other
Other intangible assets
Amortized intangible assets, carrying amount	5.7	6.0
Amortized intangible assets, accumulated amortization	5.2	5.4
Amortized intangible assets, net	$ 0.5	$ 0.6