Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Mar. 31, 2021	Sep. 30, 2020
Other intangible assets
Amortized intangible assets, carrying amount	$ 880.1	$ 795.9
Amortized intangible assets, accumulated amortization	396.7	360.3
Amortized intangible assets, net	483.4	435.6
Total, carrying amount	923.8	839.6
Total, net	527.1	479.3
Goodwill and Other Intangible Assets (Textual) [Abstract]
Estimated amortization expense, remainder of fiscal year	59.5
Estimated amortization expense in 2022	58.0
Estimated amortization expense in 2023	56.7
Estimated amortization expense in 2024	53.7
Estimated amortization expense in 2025	51.5
Trademarks
Other intangible assets
Allen-Bradley trademark not subject to amortization	43.7	43.7
Computer software products
Other intangible assets
Amortized intangible assets, carrying amount	194.5	192.7
Amortized intangible assets, accumulated amortization	144.4	139.0
Amortized intangible assets, net	50.1	53.7
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	369.1	351.3
Amortized intangible assets, accumulated amortization	108.4	92.5
Amortized intangible assets, net	260.7	258.8
Technology
Other intangible assets
Amortized intangible assets, carrying amount	224.5	165.8
Amortized intangible assets, accumulated amortization	94.2	84.0
Amortized intangible assets, net	130.3	81.8
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	76.7	71.7
Amortized intangible assets, accumulated amortization	35.4	31.3
Amortized intangible assets, net	41.3	40.4
Other
Other intangible assets
Amortized intangible assets, carrying amount	15.3	14.4
Amortized intangible assets, accumulated amortization	14.3	13.5
Amortized intangible assets, net	$ 1.0	$ 0.9