Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Dec. 31, 2021	Sep. 30, 2021
Other intangible assets
Amortized intangible assets, carrying amount	$ 1,183.8	$ 1,188.0
Amortized intangible assets, accumulated amortization	233.4	209.9
Amortized intangible assets, net	950.4	978.1
Total, carrying amount	1,227.5	1,231.7
Total, net	994.1	1,021.8
Goodwill and Other Intangible Assets (Textual) [Abstract]
Estimated amortization expense in 2022	112.3
Estimated amortization expense in 2023	110.9
Estimated amortization expense in 2024	107.9
Estimated amortization expense in 2025	105.5
Estimated amortization expense in 2026	103.9
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	88.4	90.4
Amortized intangible assets, accumulated amortization	43.5	43.2
Amortized intangible assets, net	44.9	47.2
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	595.9	595.9
Amortized intangible assets, accumulated amortization	84.9	75.4
Amortized intangible assets, net	511.0	520.5
Technology
Other intangible assets
Amortized intangible assets, carrying amount	419.4	420.8
Amortized intangible assets, accumulated amortization	84.1	71.7
Amortized intangible assets, net	335.3	349.1
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	73.1	73.8
Amortized intangible assets, accumulated amortization	14.8	13.3
Amortized intangible assets, net	58.3	60.5
Other
Other intangible assets
Amortized intangible assets, carrying amount	7.0	7.1
Amortized intangible assets, accumulated amortization	6.1	6.3
Amortized intangible assets, net	$ 0.9	$ 0.8