Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Dec. 31, 2022	Sep. 30, 2022
Other intangible assets
Amortized intangible assets, carrying amount	$ 1,212.5	$ 1,167.9
Amortized intangible assets, accumulated amortization	338.1	309.6
Amortized intangible assets, net	874.4	858.3
Total, carrying amount	1,256.2	1,211.6
Total, net	918.1	902.0
Goodwill and Other Intangible Assets (Textual) [Abstract]
Estimated amortization expense in 2022	112.9
Estimated amortization expense in 2023	110.1
Estimated amortization expense in 2024	106.8
Estimated amortization expense in 2025	105.7
Estimated amortization expense in 2026	98.8
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	98.6	97.6
Amortized intangible assets, accumulated amortization	60.2	57.9
Amortized intangible assets, net	38.4	39.7
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	598.8	582.7
Amortized intangible assets, accumulated amortization	115.9	107.2
Amortized intangible assets, net	482.9	475.5
Technology
Other intangible assets
Amortized intangible assets, carrying amount	422.8	410.8
Amortized intangible assets, accumulated amortization	133.2	119.3
Amortized intangible assets, net	289.6	291.5
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	84.7	70.4
Amortized intangible assets, accumulated amortization	22.0	19.4
Amortized intangible assets, net	62.7	51.0
Other
Other intangible assets
Amortized intangible assets, carrying amount	7.6	6.4
Amortized intangible assets, accumulated amortization	6.8	5.8
Amortized intangible assets, net	$ 0.8	$ 0.6