Goodwill and Other Intangible Assets - Other Intangibles (Details) - USD ($) $ in Millions	Sep. 30, 2024	Sep. 30, 2023
Other intangible assets
Amortized intangible assets, carrying amount	$ 1,590.9	$ 1,222.9
Amortized intangible assets, accumulated amortization	568.3	414.2
Amortized intangible assets, net	1,022.6	808.7
Total other intangible assets, carrying amount	1,634.6	1,266.6
Total other intangible assets, net	1,066.3	852.4
Software products
Other intangible assets
Amortized intangible assets, carrying amount	104.5	100.4
Amortized intangible assets, accumulated amortization	75.5	65.1
Amortized intangible assets, net	29.0	35.3
Customer relationships
Other intangible assets
Amortized intangible assets, carrying amount	619.4	606.1
Amortized intangible assets, accumulated amortization	186.5	141.3
Amortized intangible assets, net	432.9	464.8
Technology
Other intangible assets
Amortized intangible assets, carrying amount	729.1	424.1
Amortized intangible assets, accumulated amortization	257.1	173.1
Amortized intangible assets, net	472.0	251.0
Trademarks
Other intangible assets
Amortized intangible assets, carrying amount	132.0	86.3
Amortized intangible assets, accumulated amortization	43.8	29.3
Amortized intangible assets, net	88.2	57.0
Other
Other intangible assets
Amortized intangible assets, carrying amount	5.9	6.0
Amortized intangible assets, accumulated amortization	5.4	5.4
Amortized intangible assets, net	0.5	0.6
Trademarks
Other intangible assets
Allen-Bradley® trademark not subject to amortization	$ 43.7	$ 43.7