Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Mar. 31, 2024	Sep. 30, 2023
Other intangible assets
Amortized intangible assets, carrying amount	$ 1,586.6	$ 1,222.9
Amortized intangible assets, accumulated amortization	489.6	414.2
Amortized intangible assets, net	1,097.0	808.7
Total, carrying amount	1,630.3	1,266.6
Total, net	1,140.7	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	70.0	65.1
Amortized intangible assets, net	33.4	35.3
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	617.1	606.1
Amortized intangible assets, accumulated amortization	163.0	141.3
Amortized intangible assets, net	454.1	464.8
Technology
Other intangible assets
Amortized intangible assets, carrying amount	729.0	424.1
Amortized intangible assets, accumulated amortization	214.8	173.1
Amortized intangible assets, net	514.2	251.0
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	131.4	86.3
Amortized intangible assets, accumulated amortization	36.6	29.3
Amortized intangible assets, net	94.8	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