Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Dec. 31, 2020	Sep. 30, 2020
Other intangible assets
Amortized intangible assets, carrying amount	$ 877.8	$ 795.9
Amortized intangible assets, accumulated amortization	381.2	360.3
Amortized intangible assets, net	496.6	435.6
Total, carrying amount	921.5	839.6
Total, net	540.3	479.3
Goodwill and Other Intangible Assets (Textual) [Abstract]
Estimated amortization expense in 2021	59.5
Estimated amortization expense in 2022	57.9
Estimated amortization expense in 2023	56.6
Estimated amortization expense in 2024	53.6
Estimated amortization expense in 2025	51.4
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	192.7	192.7
Amortized intangible assets, accumulated amortization	141.6	139.0
Amortized intangible assets, net	51.1	53.7
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	369.4	351.3
Amortized intangible assets, accumulated amortization	102.0	92.5
Amortized intangible assets, net	267.4	258.8
Technology
Other intangible assets
Amortized intangible assets, carrying amount	223.5	165.8
Amortized intangible assets, accumulated amortization	89.3	84.0
Amortized intangible assets, net	134.2	81.8
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	76.7	71.7
Amortized intangible assets, accumulated amortization	33.8	31.3
Amortized intangible assets, net	42.9	40.4
Other
Other intangible assets
Amortized intangible assets, carrying amount	15.5	14.4
Amortized intangible assets, accumulated amortization	14.5	13.5
Amortized intangible assets, net	$ 1.0	$ 0.9