Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Dec. 31, 2023	Sep. 30, 2023
Other intangible assets
Amortized intangible assets, carrying amount	$ 1,599.8	$ 1,222.9
Amortized intangible assets, accumulated amortization	453.1	414.2
Amortized intangible assets, net	1,146.7	808.7
Total, carrying amount	1,643.5	1,266.6
Total, net	1,190.4	852.4
Goodwill and Other Intangible Assets (Textual) [Abstract]
Estimated amortization expense in 2023	153.5
Estimated amortization expense in 2024	150.0
Estimated amortization expense in 2025	148.7
Estimated amortization expense in 2026	140.6
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	105.1	100.4
Amortized intangible assets, accumulated amortization	67.8	65.1
Amortized intangible assets, net	37.3	35.3
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	618.4	606.1
Amortized intangible assets, accumulated amortization	152.2	141.3
Amortized intangible assets, net	466.2	464.8
Technology
Other intangible assets
Amortized intangible assets, carrying amount	737.6	424.1
Amortized intangible assets, accumulated amortization	194.8	173.1
Amortized intangible assets, net	542.8	251.0
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	133.0	86.3
Amortized intangible assets, accumulated amortization	33.1	29.3
Amortized intangible assets, net	99.9	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